Multiparameter Bifurcation of a Predator-Prey System
Copyright policy )Multiparameter Bifurcation of a Predator-Prey System
For a two-dimensional predator-prey system, proposed by \textit{A. D. Bazykin} [see ``Structural and dynamic stability of model predator-prey systems'' (1976; Zbl 0357.92024)] and depending on several parameters, a complete local bifurcation analysis with respect to all parameters is achieved. The major part of the paper is devoted to the unfolding of a degenerate codimension-2 bifurcation occurring for a one-dimensional subset of parameters. The main problem consists in studying parameter dependent integrals which are not algebraic.
Bifurcation theory for ordinary differential equations, Population dynamics (general), homoclinic orbits, limit cycles, two-dimensional predator-prey system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, complete local bifurcation analysis, non-algebraic parameter dependent integrals, unfolding of a degenerate codimension-2 bifurcation, Periodic solutions to ordinary differential equations
Bifurcation theory for ordinary differential equations, Population dynamics (general), homoclinic orbits, limit cycles, two-dimensional predator-prey system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, complete local bifurcation analysis, non-algebraic parameter dependent integrals, unfolding of a degenerate codimension-2 bifurcation, Periodic solutions to ordinary differential equations
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