In this paper, we introduce fractional order of a planar fractional prey-predator system with a nonmonotonic functional response and anti-predator behaviour such that the adult preys can attack vulnerable predators. We analyze the existence and stability of all possible equilibria. Numerical simulations reveal that anti-predator behaviour not only makes the coexistence of the prey and predator ...

in this paper, we introduce fractional order of a planar fractional prey-predator system with a nonmonotonic functional response and anti-predator behaviour such that the adult preys can attack vulnerable predators. we analyze the existence and stability of all possibleequilibria. numerical simulations reveal that anti-predator behaviour notonly makes the coexistence of the prey and predator po...

In this paper, we study the stability of a fractional order delayed predator-prey model. By using the Laplace transform, we introduce a characteristic equation for the above system. It is shown that if all roots of the characteristic equation have negative parts, then the equilibrium of the above fractional order predator-prey system is Lyapunov globally asymptotical stable. An example is given...

The predator-prey model with stage structure for predator is generalized in the context of ecoepidemiology, where the prey population is infected by a microparasite and the predator completely avoids consuming the infected prey. The intraspecific competition of infected prey is considered. All the equilibria are characterized and the existence of a Hopf bifurcation at the coexistence equilibriu...

This paper deals with a ratio-dependent functional response predator-prey model with a fractional order derivative. The ratio-dependent models are very interesting, since they expose neither the paradox of enrichment nor the biological control paradox. We study the local stability of equilibria of the original system and its discretized counterpart. We show that the discretized system, which is...

In this paper, we have introduced a fractional-ordered predator-prey population model which has been successfully solved with the help of two powerful analytical methods, namely, Homotopy Perturbation Method (HPM) and Variational Iteration Method (VIM). The fractional derivatives are described in the Caputo sense. Using initial values, we have derived the explicit solutions of predator-prey pop...

one may find out the application‎ ‎of mathematics in the areas of ecology‎, ‎biology‎, ‎environmental‎ ‎sciences etc‎. ‎mathematics is particulary used in the problem of‎ ‎predator-prey known as lotka-volterra predator-prey equations.‎ ‎indeed‎, ‎differential equations is employed very much in many areas‎ ‎of other sciences‎. ‎however‎, ‎most of natural problems involve some‎ ‎unknown functions...

In this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. The stages for prey have been considered. The proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. The model is analyzed by using linear stability analysis to ob...

the food chain refers to a natural system by which energy is transmitted from one organism to another. in fact, a food chain consists of producers, consumers and decomposition. presence of complex food web increase the stability of the ecosystem. classical food chain theory arises from lotka-volterra model. in the present paper, the dynamics behavior of three level food chain is studied. a syst...

the predator-prey model with stage structure for predator is generalized in the context of ecoepidemiology, where the prey population is infected by a microparasite and the predator completely avoids consuming the infected prey. the intraspecific competition of infected prey is considered. all the equilibria are characterized and the existence of a hopf bifurcation at the coexistence equilibriu...