Author: Hasan S. Panigoro, Emli Rahmi, Novianita Achmad, Sri Lestari Mahmud, R. Resmawan, Agusyarif Rezka Nuha

In this article, the dynamical behaviors of a discrete-time fractional-order Rosenzweig-MacArthur model with prey refuge are studied. The piecewise constant arguments scheme is applied to obtain the discrete-time model. All possible fixed points and their existence conditions are investigated as well as the local behavior of nearby solutions in various contingencies. Numerical simulations such as the time series, phase portraits, and bifurcation diagrams are portrayed. Three types of bifurcations are shown numerically namely the forward, the period-doubling, and Neimark-Sacker bifurcations. Some phase portraits are depicted to justify the occurrence of those bifurcations.

Published in Communications in Mathematical Biology and Neuroscience (Q3)

Author: Ismail Djakaria, Muhammad Bachtiar Gaib, Resmawan Resmawan

This paper discusses the analysis of the Rosenzweig-MacArthur predator-prey model with anti-predator behavior. The analysis is started by determining the equilibrium points, existence, and conditions of the stability. Identifying the type of Hopf bifurcation by using the divergence criterion. It has shown that the model has three equilibrium points, i.e., the extinction of population equilibrium point (E0), the non-predatory equilibrium point (E1), and the co-existence equilibrium point (E2). The existence and stability of each equilibrium point can be shown by satisfying several conditions of parameters. The divergence criterion indicates the existence of the supercritical Hopf-bifurcation around the equilibrium point E2. Finally, our model's dynamics population is confirmed by our numerical simulations by using the 4th-order Runge-Kutta methods.

Published in Cauchy (SINTA 2)