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

Datta, Soumya (2014): Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems.

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Kolmogorov-Lotka-Volterra model, predator-prey, Andronov-Hopf bifurcation, Limit cycles
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium; C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C69 - Other

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