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Chaotic evaluations in a modified coupledLogistic type predator-prey model
Published in
Volume: 6
Issue: 137-140
Pages: 6927 - 6942
Regular and chaotic oscillations in a modified discrete two dimensional coupled predator-prey model, proposed recently, is re-investigated by observing the bifurcation diagram, calculating Lyapunov exponents and correlation dimensions for various orbits. The map evolves from one cycle to three cycles followed by period doubling and then to a chaotic regime and show bistability as its parameter λ varies, 0 < ≤ 1.211. Initial population size of the species and the value their coupling coefficients play crucial role for subsequent evolutionary phenomena of the system. Regular and chaotic evolutions depend completely on the coefficient ,λ, and on the initial prey and predator population. Lyapunov exponents and correlation dimensions provide true measure of chaos and also, to identify the chaotic orbits. Some recently discovered indicators, FLI, SALI and DLI have also been used to understand the nature of orbits.Mathematical analysis have been carried out to find stable and unstable fixed points and to obtain numerical value of the parameter λ for sensitive state of the system to initial conditions i.e. emergence of chaos. Bistability condition have been discussed for variation of λ values. Graphical representation of Lyapunov exponents and correlation dimensions provide better understanding of the nature of orbits which are further justified by the use of FLI, SALI and DLI.
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