Refuge and Age Structures Impact on the Bifurcation Analysis of an Ecological Model

In this paper, the conditions of the incidence of the local bifurcation, such as a saddle-node pitchfork bifurcation and transcritical of an ecological system (consistingprey shelter (refuge) and age stages for both populations) considered to study. Lotka-Volterra type of functional response was suggested. Subsequently, the inquiry and analysis are remarked that the transcritical bifurcation transpires close to the equilibrium(symmetry) point , in addition to the incidence of asaddle-node bifurcation at symmetry points and . It should be mentioned that there is no likelihood of the incidence of the pitchfork bifurcation at every single point. In conclusion,s to illustrate the incidence of the local bifurcation of this system, some simulations were used. The aim of this study is to examine the effect of each parameter on the stability of equilibrium points.