In this paper we study bifurcations in predator-prey systems with seasonal prey harvesting. First, when the seasonal harvesting reduces to constant yield, it is shown that various kinds of bifurcations, including saddle-node bifurcation, degenerate Hopf bifurcation, and Bogdanov– Takens bifurcation (i.e., cusp bifurcation of codimension 2), occur in the model as parameters vary. The existence o...

* Correspondence: [email protected] School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, Henan, P. R. China Full list of author information is available at the end of the article Abstract For a class of fifth degree nilpotent system, the shortened expressions of the first eight quasi-Lyapunov constants are presented. It is shown that the orig...

We provide an analytical proof of the existence of a stable periodic orbit contained in the region of coexistence of the three species of a tritrophic chain. The method used consists in analyzing a triple Hopf bifurcation. For some values of the parameters three limit cycles bear via this bifurcation. One is contained in the plane where the top–predator is absent. Another one is not contained i...

In this paper, the first system of the IEEE second benchmark model (SBM) for subsynchronous resonance (SSR) studies is analyzed using the bifurcation theory. A nonlinear model for the SBM which consists of a synchronous generator connected to an infinite busbar through two parallel transmission lines, one of which is equipped with a series capacitor, has been developed in MATLAB. Generator damp...

The asymptotic behavior of a tri-trophic food chain model in the chemostat is studied. The Monod-Herbert growth model is used for all trophic levels. The analysis is carried out numerically, by finding both local and global bifurcations of equilibria and of limit cycles with respect to two chemostat control parameters: the dilution rate of the chemostat and the concentration of input substrate....

The stability analysis around equilibrium of a discrete-time predator prey system is considered in this paper. We obtain local stability conditions of the system near equilibrium points. The phase portraits are obtained for different sets of parameter values. Also limit cycles and bifurcation diagrams are provided for selective range of growth parameter. It is observed that prey and predator po...