Stability of General Systems in Biological, Physical and Social Sciences

  • G. S. Ladde
Part of the NATO Conference Series book series (NATOCS, volume 5)


The systems of nonlinear differential equations represent the mathematical model of several general systems in biological, physical and social sciences [1]. One of the most versatile techniques in the theory of nonlinear differential systems is the second method of Lyapunov [1,2]. The notion of vector Lyapunov functions, together with the theory of systems of differential inequalities, provides a very general comparison principle by means of which a number of qualitative properties of solutions of deterministic functional differential systems are studied in a unified way [3]. It is natural to expect such an extension to stochastic functional differential systems. The obtained comparison principles to stochastic functional differential systems have been utilized to study the stability behavior of hereditary stochastic general systems.


Functional Differential Equation Differential Inequality Stochastic Functional Differential Equation Vector Lyapunov Function Hereditary System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    R. Rosen, Dynamical Systems Theory in Biology, Vol. I, Wiley-Interscience, New York, 1970.Google Scholar
  2. 2.
    V. Lakshmikantham, and S. Leela, Differential and Integral Inequalities: Theory and Applications, Vol. II, Academic Press, New York, 1969.Google Scholar
  3. 3.
    G. S. Ladde, “Systems of Functional Differential Inequalities and Functional Differential Systems,” Pacific Journal of Mathematics, 66, No. 1, pp. 161–171, 1976.CrossRefGoogle Scholar
  4. 4.
    G. S. Ladde, “Competitive Processes I: Stability of Hereditary Systems,” Nonlinear Analysis: Theory, Methods and Applications, 2, 1977.Google Scholar
  5. 5.
    G. S. Ladde, and D. D. Siljak, “Stability of Multispecies Communities in Randomly Varying Environment,” Journal of Mathematical Biology, 2, pp. 165–178, 1975.CrossRefGoogle Scholar
  6. 6.
    G. S. Ladde, “Differential Inequalities and Stochastic Functional Differential Equations,” Journal of Mathematical Physics, 15, No. 6, pp. 738–743, 1974.CrossRefGoogle Scholar
  7. 7.
    L. Arnold, Stochastic Differential Equations: Theory and Applications, Wiley-Interscience, New York, 1972.Google Scholar
  8. 8.
    G. S. Ladde, “Systems of Differential Inequalities and Stochastic Differential Equations II,” Journal of Mathematical Physics, 16, No. 4, pp. 894–900, 1975.CrossRefGoogle Scholar
  9. 9.
    N. S. Goel, and N. Richter-Dyn, Stochastic Models in Biology, Academic Press, New York, 1974.Google Scholar
  10. 10.
    R. M. May, Stability and Complexity in Model Ecosystems, Princeton University Press, Princeton, 1973.Google Scholar
  11. 11.
    J. M. Smith, Models in Ecology, Cambridge University Press, Cambridge, 1974.Google Scholar

Copyright information

© Springer Science+Business Media New York 1978

Authors and Affiliations

  • G. S. Ladde
    • 1
  1. 1.Department of MathematicsSUNY at PotsdamPotsdamUSA

Personalised recommendations