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

Qiaoling Chen, Zhidong Teng, Zengyun Hu (2013)

International Journal of Applied Mathematics and Computer Science

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...

Global bifurcation of homoclinic trajectories of discrete dynamical systems

Jacobo Pejsachowicz, Robert Skiba (2012)

Open Mathematics

We prove the existence of an unbounded connected branch of nontrivial homoclinic trajectories of a family of discrete nonautonomous asymptotically hyperbolic systems parametrized by a circle under assumptions involving topological properties of the asymptotic stable bundles.

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