Displaying similar documents to “Dynamical systems analysis of a five-dimensional trophic food web model in the southern oceans.”

Limit cycles in the Holling-Tanner model.

Armengol Gasull, Robert E. Koolj, Joan Torregrosa (1997)

Publicacions Matemàtiques

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This paper deals with the following question: does the asymptotic stability of the positive equilibrium of the Holling-Tanner model imply it is also globally stable? We will show that the answer to this question is negative. The main tool we use is the computation of Poincaré-Lyapunov constants in case a weak focus occurs. In this way we are able to construct an example with two limit cycles.

Hopf-like bifurcations in planar piecewise linear systems.

Emilio Freire, Enrique Ponce, Francisco Torres (1997)

Publicacions Matemàtiques

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Continuous planar piecewise linear systems with two linear zones are considered. Due to their low differentiability specific techniques of analysis must be developed. Several bifurcations giving rise to limit cycles are pointed out.

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

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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...