Year: 2013
Type: report
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.
Author: Soumya Datta
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2172003282