The Hopf Bifurcation of the Dynamics of Behavior an Ecological Model - Dian Savitri; Abadi; Riska Romadhonia; Nurul Ah; An Nisa Salsabila; Donna Kurniasih (Jambura Journal of Biomathematics (JJBM), 2026)
We conducted a dynamic analysis of an ecological model that describes the relationship between prey and predator detritivores. Assuming that predators require more food to survive, we applied the Beddington-DeAngelis functional response to examine local stability while taking the fear effect into account. The dynamics of the local stability properties of the equilibrium point ware examined. The two population extinction points, the prey population extinction point, and all population survival were the three points that we were able to determine. The analytical computations were supported by numerical simulations. Some numerical simulations are organized to show the impact of fear effects on prey, additional food on predator and predation using Beddington-DeAngelis on the dynamical behaviors of the model. The first numerical continuation of additional food parameters in the system solution indicated the presence of a Hopf bifurcation at $A = 0.625978$. The greater the supply of additional food, the extinction of the prey that the transcitical bifurcation was found at $A = 8.694143$. The bifurcation indicated that the change remains stable, becoming unstable at the interior equilibrium point and the other system solution. The Hopf bifurcation was also found at $f= 0.081119$ according to the second numerical continuation of the fear effect parameters, and $β=1.023308$. In addition, the appearance is that the transcitical bifurcation was found at $f= 2.088891$ and $β=3.362426$. We have demonstrated numerically the occurrence of Hopf and transcritical bifurcation driven by those three biological parameters.