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In this paper, we explore the existence of fixed points, local dynamics at fixed points, bifurcations and chaos of a discrete prey-predator fishery model with harvesting. More specifically, it is proved that, for all involved parameters, the model has trivial fixed point, but it has semitrivial and interior fixed points under definite parametric condition(s). We study the local behavior at fixed points by applying the theory of linear stability. Furthermore, it is shown that flip bifurcation does not occur at semitrivial and trivial fixed points, but that the model undergoes Neimark-Sacker bifurcation at interior fixed point. It is also proved that, at interior fixed point, the model undergoes the flip bifurcation. By using a feedback control strategy, the chaos control is also examined. Finally, to illustrate the theoretical findings, detailed numerical simulations are provided. [ABSTRACT FROM AUTHOR]

We explored a local stability analysis at fixed points, bifurcations, and a control in a discrete Leslie's prey-predator model in the interior of R²+. More specially, it is examined that for all parameters, Leslie's model has boundary and interior equilibria, and the local stability is studied by the linear stability theory at equilibrium. Additionally, the model does not undergo a flip bifurcation at the boundary fixed point, though a Neimark-Sacker bifurcation exists at the interior fixed point, and no other bifurcation exists at this point. Furthermore, the Neimark-Sacker bifurcation is controlled by a hybrid control strategy. Finally, numerical simulations that validate the obtained results are given. [ABSTRACT FROM AUTHOR]

The local dynamics, chaos, and bifurcations of a discrete Brusselator system are investigated. It is shown that a discrete Brusselator system has an interior fixed point P 1 , r if r > 0. Then, by linear stability theory, local dynamical characteristics are explored at interior fixed point P 1 , r . Furthermore, for the discrete Brusselator system, the existence of periodic points is investigated. The existence of bifurcations around an interior fixed point is also investigated and proved that the discrete Brusselator model undergoes hopf and flip bifurcations if r , h ∈ ℋℬ | P 1 , r = r , h , h = 2 − r and r , h ∈ ℱℬ | P 1 , r = r , h , h = 4 / 2 − r − r 2 − 4 r , respectively. The next feedback control method is utilized to stabilize the chaos that exists in the discrete Brusselator system. Finally, obtained results are verified numerically. [ABSTRACT FROM AUTHOR]