Impact of adult predator incited fear in a stage-structured prey–predator model

The local bifurcation analysis of two preys stage-structured predator model with anti-predator behavior

“…Which represent the growth rate of first prey, the carrying capacity of second prey, the maximum predation rate of the adult predator over first and second prey respectively, the half saturation constant for second prey, the portion rate of the adult predator from second prey and the natural death rate of adult predator respectively. The parameters , are not effective on the stability of system (1) . Which represents the carrying capacity of second prey, the carrying capacity of first prey, the half saturation constant for first prey and the defense efficiency of the second prey, the grown up rate of the juvenile into adult in predator population, the portion rate of the adult predator from first and second prey, the conversion efficiency of food from the first and second prey, the anti-predator rate from second prey on the adult predator and natural death rate of the juvenile predator respectively.…”

“…̌ ̌ if the conditions (4.12)- (4.14) given in [12] and (3.12)-(3.16) hold. Hence, according to Sotomayor's theorem system (1)…”

“…To discuss the parameters effectiveness on the system's behaviour (1). By changing one parameter a time for data given in ( 5) and Table 2 summarized the results.…”

“…Bifurcation theory is an important tool for studying the effectiveness of parameters on the dynamical system and the shows the stability of equilibrium points of the model, which appears if a small change made to the parameter's value. In recent years, for the importance of the bifurcation has been considered by many researchers such as Mondal et al [1] studied a stage structured predator-prey model, also studied the stability existence and persistence and Hopf bifurcation for all the equilibrium points. Wang et al [2] studied a stage structure prey-predator model with anti-predator behaviour such that the adult prey can attack weak predators and it's observed that near the coexistence equilibrium point a Hopf bifurcation occurrence.…”

“…The numerical results of system(1) For the natural death rate of adult predator parameter . It is observed as it shown in Table2as seen in Figure.2(a-b).…”