Abstract
In this chapter we consider a simple system of two ODEs that could be used to describe various phenomena. Examples of these phenomena are presented. In general, we focus on two interacting agents, like two animal populations, two people or groups of people, two neuronal populations and so on. The system have the following structure: the first part of an equation describes the inner dynamics, while the second part is responsible for interactions. We consider two actors/agents having similar inner dynamics, as well as interaction function is similar for both of them. In the simplest case, when the inner dynamics is linear, the behavior of the system depends on the interaction functions. We discuss similarities and differences between the models with different interaction terms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Foryś, U., Bielczyk, N., Piskała, K., Płomecka, N., Poleszczuk, J.: Impact of time delay in perceptual decision-making: neuronal population modeling approach. Complexity Article ID 4391587 (2017)
Liebovitch, L., Naudot, V., Vallacher, R., Nowak, A., Biu-Wrzosinska, L., Coleman, P.: Dynamics of two-actor cooperation-competition conflict models. Physica A 387, 6360–6378 (2008)
Lotka, A.J.: Undamped oscillations derived from the law of mass action. J. Amer. Chem. Soc. 42, 1595–1599 (1920)
Murray, J.D.: Mathematical Biology: I. An Introduction. Springer, Berlin (2002)
Piotrowska, M.J., Górecka, J., Foryś, U.: The role of optimism and pessimism in the dynamics of emotional states. Discret. Contin. Dyn. Syst. Ser. B 23(1), 401–423 (2018)
Rinaldi, S., Rossa Della, F., Dercole, F., Gragnani, A., Landi P.: Modeling love dynamics. In: World Scientific Series on Nonlinear Science Series A, vol. 89. World Scientific Publishing Co. Pte. Ltd. (2015)
Smith, H.L.: Monotone dynamical systems; an introduction to the theory of competitive and cooperative systems. In: Mathematical Surveys and Monographs 41. American Mathematical Society, Providence (1993)
Strogatz, S.: Love affairs and differential equations. Math. Mag. 65(1) (1988)
Volterra, V.: Variazionie fluttuazioni del numero d’individui in specie animali conviventi. Mem. Acad. Lincei. 2, 31–113 (1926)
Volterra, V.: Variations and fluctuations of a number of individuals in animal species living together. Translation by R.N. Chapman. In: Animal Ecology, pp. 409–448. McGraw Hill, New York (1931)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Foryś, U. (2020). One Simple Model—Various Complex Systems. In: Roy, P., Cao, X., Li, XZ., Das, P., Deo, S. (eds) Mathematical Analysis and Applications in Modeling. ICMAAM 2018. Springer Proceedings in Mathematics & Statistics, vol 302. Springer, Singapore. https://doi.org/10.1007/978-981-15-0422-8_6
Download citation
DOI: https://doi.org/10.1007/978-981-15-0422-8_6
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-0421-1
Online ISBN: 978-981-15-0422-8
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)