Datta, Soumya (2014): Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems.
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Abstract
Using the AndronovHopf bifurcation theorem and the PoincaréBendixson Theorem, this paper explores robust cyclical possibilities in a generalized KolmogorovLotkaVolterra 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 AndronovHopf 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 

Original Title:  Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems 
Language:  English 
Keywords:  KolmogorovLotkaVolterra model, predatorprey, AndronovHopf 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 
Item ID:  56970 
Depositing User:  Dr. Soumya Datta 
Date Deposited:  29 Jun 2014 05:42 
Last Modified:  10 Sep 2024 21:48 
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URI:  https://mpra.ub.unimuenchen.de/id/eprint/56970 
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Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems. (deposited 20 Oct 2013 13:20)
 Robustness and Stability of Limit Cycles in a Class of Planar Dynamical Systems. (deposited 29 Jun 2014 05:42) [Currently Displayed]