Advertisement

Stability analysis of predator-prey models via Liapunov method

  • M. Gatto
  • S. Rinaldi
Medicine And Biology
Part of the Lecture Notes in Computer Science book series (LNCS, volume 40)

Abstract

As it is well known from the classical applications in the elec trical and mechanical sciences, energy is a suitable Liapunov function: thus, by analogy, all energy functions proposed in ecology are potential Liapunov functions. In this paper, a generalized Lotka-Vol terra model is considered and the stability properties of its non-tri vial equilibrium are studied by means of an energy function, first proposed by Volterra in the context of conservative ecosystems. The advantage of this Liapunov function with respect to the one that can be induced through linearization is also illustrated.

Keywords

Energy Function Global Stability Liapunov Function Positive Quadrant Positive Definite Quadratic Form 
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.

References

  1. [1]
    J.P. La Salle "Some Extensions of Liapunov's Second Method" IRE Trans. on Circuit Theory, Vol. 7, pp. 520–527, 1960.Google Scholar
  2. [2]
    R. Rosen — Dynamical System Theory in Biology Vol. 1, Wiley-Interscience, 1970.Google Scholar
  3. [3]
    E.H. Kerner "A Statistical Mechanics of Interacting Biological Species" Bull. Math. Biophys., Volume 19, pp. 121–146, 1957.Google Scholar
  4. [4]
    R.M. May — Stability and Complexity in Model Ecosystems Princeton University Press, 1973.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • M. Gatto
    • 1
  • S. Rinaldi
    • 1
  1. 1.Centro per lo Studio della Teoria dei Sistemi, C.N.R.MilanoItaly

Personalised recommendations