Open AccessCOMPLEX DYNAMIC BEHAVIORS OF A DISCRETE-TIME PREDATOR-PREY SYSTEM
Author(s) -
Ming Zhao,
Cuiping Li,
Jinliang Wang
Publication year - 2017
Publication title -
journal of applied analysis and computation
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.55
H-Index - 21
eISSN - 2158-5644
pISSN - 2156-907X
DOI - 10.11948/2017030
Subject(s) - attractor , center manifold , mathematics , chaotic , saddle node bifurcation , bifurcation , biological applications of bifurcation theory , crisis , period doubling bifurcation , invariant (physics) , hopf bifurcation , bogdanov–takens bifurcation , control theory (sociology) , complex dynamics , control of chaos , discrete time and continuous time , mathematical analysis , physics , synchronization of chaos , computer science , mathematical physics , control (management) , nonlinear system , artificial intelligence , statistics , quantum mechanics
The dynamics of a discrete-time predator–prey system is investigated in the closed first quadrant R 2 . It is shown that the system undergoes flip bifurcation and Hopf bifurcation in the interior of R 2 by using center manifold theorem and bifurcation theory. Numerical simulations are presented not only to illustrate our results with the theoretical analysis, but also to exhibit the complex dynamical behaviors, such as the period-5, 6, 9, 10, 14, 18, 20, 25 orbits, cascade of period-doubling bifurcation in period-2, 4, 8, quasi-periodic orbits and the chaotic sets. These results reveal far richer dynamics of the discrete model compared with the continuous model. The Lyapunov exponents are numerically computed to confirm further the complexity of the dynamical behaviors. 2005 Elsevier Ltd. All rights reserved.
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