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2013 | 23 | 2 | 247-261

Tytuł artykułu

Bifurcation and control for a discrete-time prey-predator model with Holling-IV functional response

Treść / Zawartość

Warianty tytułu

Języki publikacji

EN

Abstrakty

EN
The dynamics of a discrete-time predator-prey model with Holling-IV functional response are investigated. It is shown that the model undergoes a flip bifurcation, a Hopf bifurcation and a saddle-node bifurcation by using the center manifold theorem and bifurcation theory. Numerical simulations not only exhibit our results with the theoretical analysis, but also show the complex dynamical behaviors, such as the period-3, 6, 9, 12, 20, 63, 70, 112 orbits, a cascade of period-doubling bifurcations in period-2, 4, 8, 16, quasi-periodic orbits, an attracting invariant circle, an inverse period-doubling bifurcation from the period-32 orbit leading to chaos and a boundary crisis, a sudden onset of chaos and a sudden disappearance of the chaotic dynamics, attracting chaotic sets and non-attracting sets. We also observe that when the prey is in chaotic dynamics the predator can tend to extinction or to a stable equilibrium. Specifically, we stabilize the chaotic orbits at an unstable fixed point by using OGY chaotic control.

Rocznik

Tom

23

Numer

2

Strony

247-261

Opis fizyczny

Daty

wydano
2013
otrzymano
2012-04-13
poprawiono
2012-09-08

Twórcy

  • College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, People's Republic of China
autor
  • College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, People's Republic of China
autor
  • College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, People's Republic of China
  • State Key Laboratory of Desert and Oasis Ecology, Xinjiang Institute of Ecology and Geography, Chinese Academy of Sciences, Urumqi 830011, People's Republic of China

Bibliografia

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  • Duda, J. (2012). A Lyapunov functional for a system with a time-varying delay, International Journal of Applied Mathematics and Computer Science 22(2): 327-337, DOI: 10.2478/v10006-012-0024-7.
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  • Guckenheimer, J. and Holmes, P. (1983). Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, NY.
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Bibliografia

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