Skip to main content
SpringerLink
Log in

Knowledge Epidemics and Population Dynamics Models for Describing Idea Diffusion

  • Chapter
  • First Online:
Models of Science Dynamics

Part of the book series: Understanding Complex Systems ((UCS))

Abstract

The diffusion of ideas is often closely connected to the creation and diffusion of knowledge and to the technological evolution of society. Because of this, knowledge creation, exchange and its subsequent transformation into innovations for improved welfare and economic growth is briefly described from a historical point of view. Next, three approaches are discussed for modeling the diffusion of ideas in the areas of science and technology, through (i) deterministic, (ii) stochastic, and (iii) statistical approaches. These are illustrated through their corresponding population dynamics and epidemic models relative to the spreading of ideas, knowledge and innovations. The deterministic dynamical models are considered to be appropriate for analyzing the evolution of large and small societal, scientific and technological systems when the influence of fluctuations is insignificant. Stochastic models are appropriate when the system of interest is small but when the fluctuations become significant for its evolution. Finally statistical approaches and models based on the laws and distributions of Lotka, Bradford, Yule, Zipf–Mandelbrot, and others, provide much useful information for the analysis of the evolution of systems in which development is closely connected to the process of idea diffusion.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    For example, at Gordon Research Conferences, it is forbidden to take written notes and to quote participant interventions later.

  2. 2.

    For example, take the scientific disciplines and the number of publications as axes.

  3. 3.

    Let us mention a curious and interesting fact connected to statistical indicators. Very interesting is the conclusion in Gao and Guan (2009) that the scale-independent indicators show that in the fast growing innovation system of China, research institutions financed by the government play a more important role than the enterprises.

References

  • Allen JC (1975) Mathematical model of species interactions in time and space. Am Nat 109(967):319–342 (DOI: 10.1086/283000, stable JSTOR URL: http://www.jstor.org/stable/2459697)

    Google Scholar 

  • Amabile TM, Conti R, Coon H, Lazenby J, Herron M (1996) Assessing the work environment for creativity. Acad Manage Rev 39(5):1154–1184 (DOI: 10.2307/256995)

    Google Scholar 

  • Anderson RM, May RM (eds) (1982) Population biology of infectious diseases: Report of the Dahlem workshop on population biology of infectious disease agents, Berlin 1982, March 14–19. Dahlem Workshop Reports. Life Sciences Research Reports, vol 25. Springer, Berlin

    Google Scholar 

  • Antonelli C (1996) Localized knowledge percolation processes and information networks. J Evol Econ 6(3):281–295 (DOI: 10.1007/BF01193634)

    Google Scholar 

  • Ausloos M, Lambiotte R, Scharnhorst A, Hellsten I (2008) Andrzej Pȩkalski networks of scientific interests with internal degrees of freedom through self-citation analysis. Int J Mod Phys C 19(3):371–384 (DOI10.1142/S0129183108012224), also available as arXiv preprint http://arxiv.org/abs/0710.1800

    Google Scholar 

  • Ausloos M (2010) On religion and language evolutions seen through mathematical and agent based models. In: Rangacharyulu C, Haven E (eds) Proceedings of the first interdisciplinary CHESS interactions conference: Saskatoon, Saskatchewan, Canada, 17–20 August 2009. World Scientific, Singapore, pp 157–182 (DOI: 10.1142/9789814295895_0009 DOI:10.1142/9789814295895_0009), also available as arXiv preprint http://arxiv.org/abs/1103.5382arXiv:1103.5382

  • Barro RJ, Sala-i-Martin X (2004) Economic growth, 2nd edn. MIT Press, Cambridge, MA

    Google Scholar 

  • Bartholomew DJ (1982) Stochastic models for social processes, 3rd edn. Wiley Series in Probability and Mathematical Statistics. Applied Probability and Statistics. Wiley, Chichester

    Google Scholar 

  • Becker GS, Murphy KM (1988) A theory of rational addiction. J Polit Econ 96(4):675–700 (DOI: 10.1086/261558, stable JSTOR URL: http://www.jstor.org/stable/1830469)

    Google Scholar 

  • Becker GS (1996) Accounting for tastes. Harvard University Press, Cambridge, MA

    Google Scholar 

  • Bernius S (2010) The impact of open access on the management of scientific knowledge. Online Inf Rev 34(4):583–603 (DOI: 10.1108/14684521011072990)

  • Bettencourt LMA, Cintrón-Arias A, Kaiser DI, Castillo-Chávez C (2006) The power of a good idea: Quantitative modeling of the spread of ideas from epidemiological models. Physica A 364:513–536 (DOI: 10.1016/j.physa.2005.08.083), also available as arXiv preprint http://arxiv.org/abs/physics/050206

    Google Scholar 

  • Bettencourt LMA, Kaiser DI, Kaur J, Castillo-Chávez C, Wojick DE (2008) Population modeling of the emergence and development of scientific fields. Scientometrics 75(3):495–518 (DOI: 10.1007/s11192-007-1888-4)

    Google Scholar 

  • Boccaletti S, Latora V, Moreno Y, Chavez M, Hwang DU (2006) Complex networks: Structure and dynamics. Phys Rep 424(4–5):176–308 (DOI: 10.1016/j.physrep.2005.10.00)

    Google Scholar 

  • Bourdieu P (1986) Forms of capital. In: Richardson JG (ed) Handbook of theory and research for the sociology of education. Greenwood, New York, NY, pp 241–258

    Google Scholar 

  • Braun T, Glänzel W, Schubert A (1985) Scientometric indicators: A 32-country comparative evaluation of publishing performance and citation impact. World Scientific, Singapore

    Google Scholar 

  • Brauer F, Castillo-Chavez C (2001) Mathematical models in population biology and epidemiology. Texts in Applied Mathematics, vol 40. Springer, New York, NY

    Google Scholar 

  • Bruckner E, Ebeling W, Scharnhorst A (1989) Stochastic dynamics of instabilities in evolutionary systems. Syst Dyn Rev 5(2):176–191 (DOI: 10.1002/sdr.4260050206)

    Google Scholar 

  • Bruckner E, Ebeling W, Scharnhorst A (1990) The application of evolution models in scientometrics. Scientometrics 18(1):21–41 (DOI: 10.1007/BF02019160)

    Google Scholar 

  • Bruckner E, Ebeling W, Jiménez-Montaño MA, Scharnhorst A (1996) Nonlinear stochastic effects of substitution – an evolutionary approach. J Evol Econ 6(1):1–30 (DOI: 10.1007/BF01202370)

    Google Scholar 

  • Bryman A (1988) Quantity and quality in social research. Contemporary Social Research Series, vol 18. Unwin Hyman, London

    Google Scholar 

  • Burrell QL (2007) Hirsch’s h-index: A stochastic model. J Informetr 1(1):16–25 (DOI: 10.1016/j.joi.2006.07.001)

    Google Scholar 

  • Casetti E, Semple RK (1969) Concerning the testing of spatial diffusion hypotheses. Geogr Anal 1(3):254–259 (DOI: 10.1111/j.1538-4632.1969.tb00622.x)

    Google Scholar 

  • Castiaux A (2007) Radical innovation in established organizations: Being a knowledge predator. J Eng Tech Manag 24(1–2):36–52 (DOI: 10.1016/j.jengtecman.2007.01.003)

    Google Scholar 

  • Chen C, Hicks D (2004) Tracing knowledge diffusion. Scientometrics 59(2):199–211 (DOI: 10.1023/B:SCIE.0000018528.59913.48)

    Google Scholar 

  • Chen YS, Cheng PP, Tong Y (1993) Theoretical foundation of the 80/20 rule. Scientometrics 28(2):183–204 (DOI: 10.1007/BF02016899)

    Google Scholar 

  • Chung KH, Cox RAK (1990) Patterns of productivity in the finance literature: A study of the bibliometric distributions. J Finance 45(1):301–309 (DOI: 10.2307/2328824DOI:10.2307/2328824, stable JSTOR URL: http://www.jstor.org/stable/2328824)

    Google Scholar 

  • Coleman JC (1988) Social capital in the creation of human capital. Am J Sociol 94(Suppl):S95–S120. (DOI: 10.1086/228943, stable JSTOR URL: http://www.jstor.org/stable/2780243)

    Google Scholar 

  • Cowan R, Foray D (1997) The economics of codification and the diffusion of knowledge. Ind Corp Change 6(3):595–622 (DOI: 10.1093/icc/6.3.595)

    Google Scholar 

  • Dahlman C, Zhihua Zeng D, Wang S (2007) Enhancing China’s competitiveness through life long learning. The World Bank, Washington, DC

    Book  Google Scholar 

  • Dahlman C (2009) Different innovation strategies, different results: Brazil, Russia, India, China and Korea (the BRICKs). In: Chandra V, Eröcal D, Padoan PC, Primo Braga AC (eds) Innovation and growth: Chasing a moving frontier. OECD, Paris; International Bank for Reconstruction and Development/The World Bank, Washington, DC, pp 131–168, available online at the URL: http://www.oecd.org/document/35/0,3343,en_2649_37417_44268835_1_1_1_37417,00.html

  • Daley DJ (1967) Concerning the spread of news in a population of individuals who never forget. Bull Math Biol 29(2):373–376 (DOI: 10.1007/BF02476908)

  • Davis JB (2003) The theory of the individual in economics: Identity and value. Routledge Advances in Social Economics. Routledge, London (DOI: 10.4324/9780203457689)

  • Dietz K (1967) Epidemics and rumours: A survey. J R Stat Soc Ser A 130(4):505–528 (DOI: 10.2307/2982521, stable JSTOR URL: http://www.jstor.org/stable/2982521)

  • Dimitrova ZI, Vitanov NK (2000) Influence of adaptation on the nonlinear dynamics of a system of competing populations. Physc Lett A 272(5–6):368–380 (DOI: 10.1016/S0375-9601(00)00455-2)

  • Dimitrova ZI, Vitanov NK (2001) Adaptation and its impact on the dynamics of a system of three competing populations. Physica A 300(1–2):91–115 (DOI: 10.1016/S0378-4371(01)00330-2)

  • Dimitrova ZI, Vitanov NK (2001) Dynamical consequences of adaptation of the growth rates in a system of three competing populations. J Phys A Math Gen 34(37):7459–7473 (DOI: 10.1088/0305-4470/34/37/303)

    Google Scholar 

  • Dimitrova ZI, Vitanov NK (2004) Chaotic pairwise competition. Theor Popul Biol 66(1):1–12 (DOI: 10.1016/j.tpb.2003.10.008)

    Google Scholar 

  • Dodd SC (1958) Formulas for spreading opinions. Public Opin Q 22(4):537–554 (DOI: 10.1086/266827, stable JSTOR URL: http://www.jstor.org/stable/2746601)

  • Dolfsma W (2008) Knowledge economies: Organization, location and innovation. Routledge Studies in Global Competition, vol 39. Routledge, London

    Google Scholar 

  • Ebeling W, Engel A, Mazenko VG (1986) Modeling of selection processes with age-dependent birth and death rates. BioSystems 19(3):213–221 (DOI: 10.1016/0303-2647(86)90040-7)

    Google Scholar 

  • Ebeling W, Engel A, Feistel R (1990) Physik der Evolutionsprozesse. Akademie-Verlag, Berlin

    Google Scholar 

  • Ebeling W, Feistel R, Hartmann-Sonntag I, Schimansky-Geier L, Scharnhorst A (2006). New species in evolving networks – stochastic theory of sensitive networks and applications on the metaphorical level. BioSystems 85(1):65–71 (DOI: 10.1016/j.biosystems.2006.02.013)

    Google Scholar 

  • Ebeling W, Scharnhorst A (1985) Selforganization models for field mobility of physicists. Czech J Phys 36(1):43–46 (DOI: 10.1007/BF01599723)

    Google Scholar 

  • Ebeling W, Scharnhorst A (2000) Evolutionary models of innovation dynamics. In: Helbing D, Herrmann HJ, Schreckenberg M, Wolf DE (eds) Traffic and granular flow’ 99. Social, traffic and granular dynamics. Springer, Berlin, pp 43–56

    Google Scholar 

  • Edelstein-Keshet L (1988) Mathematical models in biology. The Random House/Birkhäuser Mathematics Series. Random House, New York, NY

    Google Scholar 

  • Egghe L (1998) Mathematical theories of citation. Scientometrics 43(1):57–62 (DOI: 10.1007/BF02458394)

    Google Scholar 

  • Egghe L, Rousseau R (1990) Introduction to informetrics: Quantitative methods in library, documentation and information science. Elsevier, Amsterdam

    Google Scholar 

  • Epstein JM (1997) Nonlinear dynamics, mathematical biology, and social science. Santa Fe Institute Studies in the Sciences of Complexity. Lecture Note, vol 4. Addison-Wesley, Reading, MA

    Google Scholar 

  • Fernández-Camo A, Toralbo M, Vallejo M (2004) Reconsidering Price’s model of scientific growth: An overview. Scientometrics 61(3):301–321 (DOI: 10.1023/B:SCIE.0000045112.11562.11)

    Google Scholar 

  • Foray D (2004) The economics of knowledge. MIT Press, Cambridge, MA. Revised and extended translation of: Foray D (2000) L’conomie de la connaissance. La Decouverte, Paris

    Google Scholar 

  • Gao X, Guan J (2009) A scale-independent analysis of the performance of the Chinese innovation system. J Informetr 3(4):321–331 (DOI: 10.1016/j.joi.2009.04.004)

    Google Scholar 

  • Gardiner CW (1983) Handbook of stochastic methods for physics, chemistry and the natural sciences. Springer Series in Synergetics, vol 13. Springer, Berlin

    Google Scholar 

  • Gause GF (1934) The struggle for existence. Williams and Wilkins, Baltimore, MD

    Book  Google Scholar 

  • Geroski PA (2000) Models of technology diffusion. Res Policy 29(4):603–625 (DOI: 10.1016/S0048-7333(99)00092-X)

    Google Scholar 

  • Gilbert GN (1978) Measuring the growth of science: A review of indicators of scientific growth. Scientometrics 1(1):9–34 (DOI: 10.1007/BF02016837)

    Google Scholar 

  • Glänzel W, Schoepflin U (1994) A stochastic model for the ageing of scientific literature. Scientometrics 30(1):49–64 (DOI: 10.1007/BF02017212)

    Google Scholar 

  • Goffman W (1966) Mathematical approach to the spread of scientific ideas – the history of mast cell research. Nature 212(5061):449–452 (DOI: 10.1038/212449a0)

    Google Scholar 

  • Goffman W, Newill VA (1964) Generalization of epidemic theory: An application to the transmission of ideas. Nature 204(4955):225–228 (DOI: 10.1038/204225a0)

    Google Scholar 

  • Haitun SD (1982) Stationary scientometric distributions. Part II. Non-Gaussian nature of scientific activities. Scientometrics 4(2):89–104 (DOI: 10.1007/BF02018448)

    Google Scholar 

  • Hänggi P, Thomas H (1982) Stochastic processes: Time evolution, symmetries and linear response. Phys Rep 88(4):207–319 (DOI: 10.1016/0370-1573(82)90045-X)

  • Hellsten I, Lambiotte R, Scharnhorst A, Ausloos M (2006) A journey through the landscape of physics and beyond – the self-citation patterns of Werner Ebeling. In: Pöschel T, Malchow H, Schimansky–Geier L (eds) Irreversible Prozesse und Selbstorganisation. Logos Verlag, Berlin, pp 375–384

    Google Scholar 

  • Hellsten I, Lambiotte R, Scharnhorst A, Ausloos M (2007) Self-citations, co-authorships and keywords: A new method for detecting scientists field mobility? Scientometrics 72(3):469–486 (DOI: 10.1007/s11192-007-1680-5)

  • Hellsten I, Lambiotte R, Scharnhorst A, Ausloos M (2007) Self-citation networks as traces of scientific careers. In: Torres-Salinas D, Moed H (eds) Proceedings of the ISSI 2007, 11th International Conference of the International Society for Scientometrics and Informetrics, CSIC, Madrid, Spain, June 25–27, 2007. CINDOC-CSIC, Madrid, vol 1, pp 361–367

    Google Scholar 

  • Hirsch JE (2005) An index to quantify an individual’s scientific research output. Proc Natl Acad Sci USA 102(46):16569–16572 (DOI: 10.1073/pnas.0507655102, stable JSTOR URL: http://www.jstor.org/stable/4152261), also available as arXiv preprint http://arxiv.org/abs/physics/0508025

    Google Scholar 

  • Howells JRL (2002) Tacit knowledge, innovation and economic geography. Urban Stud 39(5–6):871–884 (DOI: 10.1080/00420980220128354)

    Google Scholar 

  • Ivanova K, Ausloos M (1999) Application of the detrended fluctuation analysis (DFA) method for describing cloud breaking. Physica A 274(1–2):349–354 (DOI: 10.1016/S0378-4371(99)00312-X)

  • Jaffe AB (1986) Technological opportunity and spillovers of R&D: Evidence from firms patents, profits, and market value. Am Econ Rev 76(5):984–1001 (stable JSTOR URL: http://www.jstor.org/stable/1816464), also availabe online as National Bureau of Economic Research (NBER) Working Paper No. 1815 at the URL: http://www.nber.org/papers/w1815

  • Jaffe AB, Trajtenberg M (eds) (2002) Patents, citations and innovations: A window on the knowledge economy. MIT Press, Cambridge, MA

    Google Scholar 

  • Karmeshu (1982) Time lag in a diffusion model of information. Math model 3(2):137–141 (DOI: 10.1016/0270-0255(82)90018-5)

  • Katz JS (1999) The self-similar science system. Res Policy 28(5):501–517 (DOI: 10.1016/S0048-7333(99)00010-4)

    Google Scholar 

  • Kealey T (2000) More is less. Economists and governments lag decades behind Derek Price’s thinking. Nature 405(6784):279–279 (DOI: 10.1038/35012717)

    Google Scholar 

  • Kermack WO, McKendrick AG (1927) A contribution to the mathematical theory of epidemics. Proc R Soc Lond A Math Phys Character 115(772):700–721 (DOI: 10.1098/rspa.1927.0118, stable JSTOR URL: http://www.jstor.org/stable/94815)

  • Kerner EH (1959) Further considerations on the statistical mechanics of biological associations. Bull Math Biol 21(2):217–253 (DOI: 10.1007/BF02476361)

    Google Scholar 

  • Keynes JM (1930) A treatise on money. 2 Volumes. Harcourt, Brace and Co., New York, NY. Reprinted in: Keynes JM (1971, 1989, 2nd edn) The collected writings of John Maynard Keynes: Volume V: A treatise on money: In two volumes: 1. The pure theory of money, Volume VI: A treatise on money: In two volumes: 2. The applied theory of money. Macmillan, London

    Google Scholar 

  • Kiss IZ, Broom M, Graze PG, Rafols I (2000) Can epidemic models describe the diffusion of topics across disciplines. J Infometr 4(1):74–82 (DOI: 10.1016/j.joi.2009.08.002), also available as arXiv preprint http://arxiv.org/abs/0905.3585

    Google Scholar 

  • Kiss IZ, Green DM, Kao RR (2005) Disease contact tracing in random and clustered networks. Proc R Soc B Biol Sci 272(1570):1407–1414 (DOI: 10.1098/rspb.2005.3092, stable JSTOR URL: http://www.jstor.org/stable/30047699)

    Google Scholar 

  • Kot SM (1987) The stochastic model of evolution of scientific disciplines. Scientometrics 12(3–4):197–205 (DOI: 10.1007/BF02016292)

    Google Scholar 

  • Kucharavy D, Schenk E, de Guio R (2009) Long-run forecasting of emerging technologies with logistic models and growth of knowledge. In: Roy R, Shehab E (eds) Proceedings of the 19th CIRP design conference – competitive design, Cranfield, UK. Cranfield University, Cranfield, pp 277–284, available online at the URL: http://dspace.lib.cranfield.ac.uk/handle/1826/3730

  • Kuhn TS (1962) The structure of scientific revolutions. University of Chicago Press, Chicago, IL

    Google Scholar 

  • Lal VB, Karmeshu, Kaicker S (1988) Modeling innovation diffusion with distributed time lag. Technol Forecast Soc Change 34(2):103–113 (DOI: 10.1016/0040-1625(88)90060-1)

  • Leydesdorff L (2006) The knowledge-based economy: Modeled, measured, simulated. Universal Publishers, Boca Raton, FL

    Google Scholar 

  • Li W (2002) Zipf’s law everywhere. Glottometrics 5:15–41, available online at the URL: http://www.nslij-genetics.org/wli/pub/glottometrics02.pdf

    Google Scholar 

  • Lotka AJ (1912) Ein Fall von Autokatakinese mit oscillatorischem Verlauf. Zeitschrift für Physikalische Chemie, Stöchiometrie und Verwandtschaftslehre 80(2):159–164

    Google Scholar 

  • Lotka AJ (1925) Elements of physical biology. Williams & Wilkins Company, Baltimore, MD, available online at the URL: http://www.archive.org/details/elementsofphysic017171mbp. Reprinted as: Lotka AJ (1956) Elements of mathematical biology. Dover Books on the Biological Sciences. Dover Publications, New York, NY

  • Lotka AJ (1926) The frequency distribution of scientific productivity. J Wash Acad Sci 16(12):317–323

    Google Scholar 

  • Ma Z, Li J (eds) (2009) Dynamical modeling and analysis of epidemics. World Scientific, Singapore, available online at the URL: http://ebooks.worldscinet.com/ISBN/9789812797506/9789812797506.html

  • Magyari-Beck I (1984) A method of measurement of scientific production quality. Science of Science 4(2):183–195

    Google Scholar 

  • Mahajan V, Peterson RA (1985) Models for innovation diffusion. Quantitative Applications in the Social Sciences, vol 48. Sage Publications, Beverly Hills, CA

    Google Scholar 

  • Mansfield E (1961) Technical change and the rate of imitation. Econometrica 29(4):741–766 (DOI: 10.2307/1911817, stable JSTOR URL: http://www.jstor.org/stable/191181)

    Google Scholar 

  • Marshall A (1920) Principles of economics: An introductory volume, 8th edn. McMillan, London, available online ((1907) 5th edn) at the URL: http://www.archive.org/details/principlesofecon01marsuoft

  • May RM (1974) Stability and complexity in model ecosystems, 2nd edn. Monographs in Population Biology, vol 6. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Meade N, Islam T (1995) Forecasting with growth curves: An empirical comparison. Int J Forecast 11(2):199–215 (DOI: 10.1016/0169-2070(94)00556-R)

    Google Scholar 

  • Meyer PS (1994) Bi-logistic growth. Technol Forecast Soc Change 47(1):89–102 (DOI: 10.1016/0040-1625(94)90042-6)

  • Meyer PS, Yung JW, Ausubel JH (1999) A primer on logistic growth and substitution: The mathematics of the Loglet Lab software. Technol Forecast Soc Change 61(3):247–271 (DOI: 10.1016/S0040-1625(99)00021-9)

  • Modis T (2003) A scientific approach to managing competition. Ind Physicist 9(1):24–27, available online at the URL: http://www.aip.org/tip/INPHFA/vol-9/iss-1/p25.html

    Google Scholar 

  • Modis T (2007) Strengths and weaknesses of S-curves. Technol Forecast Soc Change 74(6):866–872 (DOI: 10.1016/j.techfore.2007.04.005)

  • Morone P, Taylor R (2010) Knowledge diffusion and innovation: Modelling complex entrepreneurial behaviours. Edward Elgar Publishing Inc., Northampton, MA

    Google Scholar 

  • Murray JD (1989) Mathematical biology. Biomathematics, vol 19. Springer, Berlin

    Google Scholar 

  • Nonaka I (1994) A dynamic theory of organizational knowledge creation. Organ Sci 5(1):14–37 (DOI: 10.1287/orsc.5.1.14, stable JSTOR URL: http://www.jstor.org/stable/2635068)

    Google Scholar 

  • Nonaka I, Takeuchi H (1995) The knowledge creating company: How Japanese companies create the dynamics of innovation. Oxford University Press, Oxford

    Google Scholar 

  • Nonaka I, Konno N (1998) The concept of “Ba”: Building a foundation for knowledge creation. Calif Manage Rev 40(3):40–54 (DOI: 10.1225/CMR107)

    Google Scholar 

  • Nowakowska M (1973) Epidemical spread of scientific objects: An attempt of empirical approach to some problems of meta-science. Theory Decis 3(3):262–297 (DOI: 10.1007/BF00139506)

    Google Scholar 

  • Noyons ECM, Van Raan AFJ (1998) Advanced mapping of science and technology. Scientometrics 41(1–2):61–67 (DOI: 10.1007/BF02457967)

    Google Scholar 

  • Odum EP (1959) Fundamentals of ecology. W.B. Saunders, Philadelphia, PA

    Google Scholar 

  • Okubo A (1980) Diffusion and ecological problems: Mathematical models. Biomathematics, vol 10. Springer, Berlin. Extended translation of: Okubo A (1975) Seitaigaku to kakusan. Tukijishokan, Tokyo

    Google Scholar 

  • Plesk PE (1997) Creativity, innovation and quality. ASQ Quality Press, Milwaukee, WI

    Google Scholar 

  • Price DJ de Solla (1951) Quantitative measures of the development of science. Archives Internationale d’Histoire de Sciences 4(14):86–93, available online at the URL: http://garfield.library.upenn.edu/price/pricequantitativemeasures1951.pdf

  • Price DJ de Solla (1956) The exponential curve of science. Discovery 17(1):240–243. Reprinted in: Barber B, Hirsch W (eds) (1962) The sociology of science. The Free Press of Glencoe, New York, NY, pp 516–524

    Google Scholar 

  • Price DJ de Solla (1961) Science since Babylon. Yale University Press, New Haven, CT

    Google Scholar 

  • Price DJ de Solla (1963) Little science, big science. Columbia University Press, New York, NY

    Google Scholar 

  • Price DJ de Solla (1971) Principles for projecting funding of academic science in the 1970s. Sci Stud 1(1):85–94 (DOI: 10.1177/030631277100100106, stable JSTOR URL: http://www.jstor.org/stable/370198)

  • Price DJ de Solla (1976) A general theory of bibliometric and other cumulative advantage processes. J Am Soc Inf Sci 27(5):292–306 (DOI: 10.1002/asi.4630270505), also available online at the URL: http://www.asis.org/Publications/JASIS/Best\_Jasist/1976pricejasistarticle.pdf

  • Price DJ de Solla, Gürsey S (1975) Some statistical results for the numbers of authors in the states of the United States and the nations of the world. In: Who is publishing in science 1975 annual. Institute for Scientific Information, Philadelphia, PA, pp 26–34

    Google Scholar 

  • Putnam RD, Leonardi R, Nanetti RY (1993) Making democracy work: Civic transitions in modern Italy. Princeton University Press, Princeton, NJ

    Google Scholar 

  • Risken H (1984) The Fokker-Planck equation: Methods of solution and applications. Springer Series in Synergetics, vol 18. Springer-Verlag, Berlin

    Google Scholar 

  • Rogers E (1962) Diffusion of innovations. The Free Press, New York, NY; Collier-MacMillan, London

    Google Scholar 

  • Romanov AK, Terekhov AI (1997) The mathematical model of productivity- and age-structured scientific community evolution. Scientometrics 39(1):3–17 (DOI: 10.1007/BF02457427)

    Google Scholar 

  • Romer PM (2002) When should we use intellectual property rights? Am Econ Rev 92(2):213–216 (DOI: 10.1257/000282802320189276, stable JSTOR URL: http://www.jstor.org/stable/3083404). The article is part of: Baldwin JE, Oaxaca RL (eds) Papers and proceedings of the one hundred fourteenth annual meeting of the American Economic Association, Atlanta, GA, January 4–6, 2002. Am Econ Rev 92(2):1–478

    Google Scholar 

  • Romer PM (1994a) The origins of endogeneous growth. J Econ Perspect 8(1):3–22 (stable JSTOR URL: http://www.jstor.org/stable/2138148)

    Google Scholar 

  • Romer PM (1994b) New goods, old theory, and the welfare costs of trade restrictions. J Dev Econ 43(1):5–38 (DOI: 10.1016/0304-3878(94)90021-3), also availabe online as National Bureau of Economic Research (NBER) Working Paper No. 4452 at the URL: http://www.nber.org/papers/w4452

    Google Scholar 

  • Romer D (1996) Advanced macroeconomics. McGraw-Hill, New York, NY

    Google Scholar 

  • Saviotti PP (1999) Knowledge, information and organisational structures. In: Robertson PL (ed) Authority and control in modern industry: Theoretical and empirical perspectives. Routledge Studies in Business Organization and Networks, vol 10. Routledge, London, pp 120–139 (DOI: 10.4324/9780203435403.ch4)

  • Scharnhorst A (1998) Citation networks, science landscapes and evolutionary strategies. Scientometrics 43(1):95–106 (DOI: 10.1007/BF02458399)

    Google Scholar 

  • Scharnhorst A (2001) Constructing knowledge landscapes within the framework of geometrically oriented evolutionary theories. In: Matthies M, Malchow H, Kriz J (eds) Integrative systems approaches to natural and social dynamics. Springer, Berlin, pp 505–515

    Chapter  Google Scholar 

  • Sharif MN, Ramanathan K (1981) Binomial innovation diffusion models with dynamic potential adopter population. Technol Forecast Soc Change 20(1):63–87 (DOI: 10.1016/0040-1625(81)90041-X)

  • Small H (1997) Update on science mapping: Creating large document spaces. Scientometrics 38(2):275–293 (DOI: 10.1007/BF02457414)

    Google Scholar 

  • Small H (1998) A general framework for creating large-scale maps of science in two or three dimensions: The SciViz system. Scientometrics 41(1–2):125–133 (DOI: 10.1007/BF02457973)

    Google Scholar 

  • Small H (2006) Tracking and predicting growth areas in science. Scientometrics 68(3):595–610 (DOI: 10.1007/s11192-006-0132-y)

    Google Scholar 

  • Soler JM (2007) A rational indicator of scientific creativity. J Informetr 1(2):123–130 (DOI: 10.1016/j.joi.2006.10.004), also available as arXiv preprint http://arxiv.org/abs/physics/0608006

    Google Scholar 

  • Solomon S, Richmond P (2001) Power laws of wealth, market order volumes and market returns. Physica A 299(1–2):188–197 (DOI: 10.1016/S0378-4371(01)00295-3), also available as arXiv preprint http://arxiv.org/abs/cond-mat/0102423

  • Solomon S, Richmond P (2002) Stable power laws in variable economics; Lotka–Volterra implies Pareto–Zipf. Eur Phys J B 27(2):257–261 (DOI: 10.1140/epjb/e20020152)

    Google Scholar 

  • Stiglitz JE (1987) Learning to learn, localized learning and technological progress. In: Dasgupta P, Stoneman P (eds) Economic policy and technological performance. Cambridge University Press, Cambridge, pp 125–153

    Chapter  Google Scholar 

  • Szydlowski M, Krawiez A (2001) Scientific cycle model with delay. Scientometrics 52(1):83–95 (DOI: 10.1023/A:1012751028630)

    Google Scholar 

  • Szydlowski M, Krawiez A (2009) Growth cycles of knowledge. Scientometrics 78(1):99–111 (DOI: 10.1007/s11192-007-1958-7)

    Google Scholar 

  • Vandewalle N, Ausloos M (1997) Coherent and random sequences in financial fluctuations. Physica A 246(3–4):454–459 (DOI: 10.1016/S0378-4371(97)00366-X)

    Google Scholar 

  • van Kampen NG (1981) Stochastic processes in physics and chemistry. North-Holland Publishing Company, Amsterdam

    Google Scholar 

  • van Raan AFJ (1997) Scientometrics: State of art. Scientometrics 38(1):205–218 (DOI: 10.1007/BF02461131)

    Google Scholar 

  • van Raan AFJ (2000) On growth, ageing and fractal differentiation of science. Scientometrics 47(2):347–362 (DOI: 10.1023/A:1005647328460)

    Google Scholar 

  • Vitanov NK, Dimitrova ZI, Kantz H (2006) On the trap of extinction and its elimination. Phys Lett A 349(5):350–355 (DOI: 10.1016/j.physleta.2005.09.043)

    Google Scholar 

  • Vitanov NK, Dimitrova ZI, Ausloos M (2010) Verhulst-Lotka–Volterra (VLV) model of ideological struggle. Physica A 389(21):4970–4980 (DOI: 10.1016/j.physa.2010.06.032), also available as arXiv preprint http://arxiv.org/abs/1103.5362

    Google Scholar 

  • Vitanov NK, Jordanov IP, Dimitrova ZI (2009) On nonlinear population waves. Appl Math Comput 215(8):2950–2964 (DOI: 10.1016/j.amc.2009.09.041)

    Google Scholar 

  • Vitanov NK, Jordanov IP, Dimitrova ZI (2009) On nonlinear dynamics of interacting populations: Coupled kink waves in a system of two populations. Commun Nonlinear Sci Numer Simul 14(5):2379–2388 (DOI: 10.1016/j.cnsns.2008.07.015)

    Google Scholar 

  • Volterra V (1927) Variazioni e fluttuazioni del numero d’individui in specie animali conviventi. Memorie della Classe di Scienze Fisiche, Matematiche e Naturali, Accademia Nazionale dei Lincei, Roma, 6th series, 2(3):31–113. English translation: Variations and fluctuations of the number of individuals in animal species living together. In: Chapman RN (1931) Animal ecology. McGraw Hill, New York, NY, pp 409–448

    Google Scholar 

  • Wagner-Döbler R, Berg J (1994) Regularity and irregularity in the development of scientific disciplines: The case of mathematical logics. Scientometrics 30(1):303–319 (DOI: 10.1007/BF02017230)

    Google Scholar 

  • Walsh JR (1935) Capital concept applied to man. Q J Econ 49(2):255–285 (DOI: 10.2307/1884067, stable JSTOR URL: http://www.jstor.org/stable/1884067)

  • Willson WG, de Roos AM (1993) Spatial instabilities within the diffusive Lotka–Volterra system: Individual-based simulation results. Theor Popul Biol 43(1):91–127 (DOI: 10.1006/tpbi.1993.1005)

    Google Scholar 

  • Wright S (1932) The roles of mutation, inbreeding, crossbreeding and selection in evolution. In: Jones DF (ed) Proceedings of the Sixth International Congress of Genetics. Brooklyn Botanic Garden, Brooklyn, NY, part 1, pp 356–366, available online at the URL: http://www.esp.org/books/6th-congress/facsimile/contents/6th-cong-p356-wright.pdf

  • Yablonsky AI (1980) On fundamental regularities of the distribution of scientific productivity. Scientometrics 2(1):3–34 (DOI: 10.1007/BF02016597)

    Google Scholar 

  • Yablonsky AI (1985) Stable non-Gaussian distributions in scientometrics. Scientometrics 7(3–6):459–470 (DOI: 10.1007/BF02017161)

    Google Scholar 

  • Ziman JM (1969) Information, communication, knowledge. Nature 224(5217):318–324 (DOI: 10.1038/224318a01)

    Google Scholar 

  • Zipf GK (1949) Human behavior and the principle of least effort: An introduction to human ecology. Addison-Wesley, Cambridge, MA

    Google Scholar 

Download references

Acknowledgements

Thanks to the editors of the book for inspiring us into writing this work. The authors gratefully acknowledge stimulating discussions with many wonderful colleagues at several meetings of the ESF Action COST MP-0801 ‘Physics of Competition and Conflict’.

Author information

Authors and Affiliations

  1. Institute of Mechanics, Bulgarian Academy of Sciences, Akad. G. Bonchev Str., Bl. 4, 1113, Sofia, Bulgaria

    Nikolay K. Vitanov

  2. 7 rue des Chartreux, B-4122, Plainevaux, Belgium

    Marcel R. Ausloos

  3. Previously at GRAPES, SUPRATECS, University of Liege, B-4000, Liege, Belgium

    Marcel R. Ausloos

Authors
  1. Nikolay K. Vitanov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marcel R. Ausloos
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nikolay K. Vitanov .

Editor information

Editors and Affiliations

  1. Humanities and Social Sciences, Royal Neth. Academy of Arts a. Sciences, The Virtual Knowledge Studio for the, Cruquiusweg 31, Amsterdam, 1019 AT, Netherlands

    Andrea Scharnhorst

  2. Center, School of Library and Information Sc., Cyberinfrastructure for Network Science, 10th Street and Jordan Avenue, Bloomington, 47405, USA

    Katy Börner

  3. The Rathenau Institute, Science System Assessment Center, Anna van Saksenlaan 51, The Hague, 2593 HW, Netherlands

    Peter van den Besselaar

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Vitanov, N.K., Ausloos, M.R. (2012). Knowledge Epidemics and Population Dynamics Models for Describing Idea Diffusion. In: Scharnhorst, A., Börner, K., van den Besselaar, P. (eds) Models of Science Dynamics. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23068-4_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-23068-4_3

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23067-7

  • Online ISBN: 978-3-642-23068-4

  • eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)

Publish with us

Policies and ethics

Search

Navigation