Skip to main content
Article thumbnail
Location of Repository

Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems

By Soumya Datta

Abstract

Using the Andronov-Hopf bifurcation theorem and the Poincaré-Bendixson Theorem, this paper explores robust cyclical possibilities in a generalized Kolmogorov-Lotka-Volterra class of models with positive intraspecific cooperation in the prey population. This additional feedback effect introduces nonlinearities which modify the cyclical outcomes of the model. Using an economic example, the paper proposes an algorithm to symbolically construct the topological normal form of Andronov-Hopf bifurcation. In case the limit cycle turns out to be unstable, the possibilities of the dynamics converging to another limit cycle is explored.

Topics: C62 - Existence and Stability Conditions of Equilibrium, C69 - Other
Year: 2014
OAI identifier: oai:mpra.ub.uni-muenchen.de:56970

Suggested articles


To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.