In this paper, a mathemat ical model is proposed to study the effect of exotic predator population on a system of native prey-predator population. The model includes three state variables viz., density of native prey, density of native predator and density of exotic predator. The stability analysis of all the feasible equilibria are carried out and also the possibility of Hopf-bifu rcation of the interior equilibriu m point is investigated for the parameter 2 ; the predation rate of exotic predator. By vary ing the parameter 2 , a change in stability behaviour of the interior equilibriu m is also observed. The stability and direction of bifurcating periodic solution is discussed. Finally the analytical results are supported by numerical simulat ion.
In this paper, a system consisting of two competing harmfu l phytoplankton and a zooplankton with Holling type-II functional response and discrete time lag is considered. A stable co-existence of all the species has been observed for the system without delay and the Hopf-b ifurcation phenomenon is observed for the interior equilibriu m po int. The Hopf-bifurcating solution is obtained for the critical values of parameters like predation rates and half saturation constants. Further, using the normal form theory, we have determined the direction and the stability of the Hopf-bifurcation solution. The introduction of time delay in the system also shows the Hopf-bifurcat ion as the delay parameter passes through a critical value. Finally, the numerical simu lation is carried out to support the theoretical results.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.