Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-09T13:22:35.972Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic behaviour of a class of discontinuous difference equations

Published online by Cambridge University Press:  17 February 2009

M. E. Fisher  and
P. E. Kloeden
M. E. Fisher
Affiliation:
Department of Mathematics, University of W.A., Nedlands, Western Australia, 6009
P. E. Kloeden
Affiliation:
School of Mathematical and Physical Sciences, Murdoch University, Murdoch, Western Australia, 6153
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Sufficient conditions for an equilibrium point to be an attractor or a global attractor are derived for a class of first-order difference equations which need not be continuous at the equilibrium point. These conditions involve Lyapunovlike functions which need not be continuous and are applied to the logistic equation with a piecewise continuous control.

Type
Research Article
Information
The ANZIAM Journal , Volume 20 , Issue 3 , June 1978 , pp. 370 - 374
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Fisher, M. E., Goh, B. S. and Vincent, T. L., “Some stability conditions for discrete time single species models’, to appear in Bull. Math. Biology.Google Scholar
[2]Goh, B. S., Leitmann, G. and Vincent, T. L., “Optimal control of a predator-prey system’, Mathematical Biosciences 19 (1974), 263–286.Google Scholar
[3]La Salle, J. P., The stability of dynamical systems, Regional Conference Series in Applied Mathematics, S.I.A.M., Philadelphia (1976).Google Scholar
[4]Pielou, E. C., An introduction to mathematical ecology (Wiley-Interscience, New York, 1969).Google Scholar