Abstract This paper is about to formulate a design of predator–prey model with constant and time fractional variable order. The predator prey act as agents in an ecosystem this simulation. We focus on order Atangana–Baleanu operator the sense Liouville–Caputo. Due nonlocality method, generated by using another FO derivative developed kernel based generalized Mittag-Leffler function. Two fractio...

In this paper, a modified Leslie–Gower predator-prey model with Beddington–DeAngelis functional response and double Allee effect in the growth rate of predator population is proposed. order to consider memory on proposed model, we employ Caputo fractional-order derivative. We investigate dynamic behaviors for both strong weak cases. The existence, uniqueness, non-negativity, boundedness solutio...

This paper discusses a predator-prey system with Holling-(n + 1) functional response and the fractional type nonlinear diffusion term in a bounded domain under homogeneous Neumann boundary condition.The existence and nonexistence results concerning nonconstant positive steady states of the system were obtained. In particular, we prove that the positive constant solution (?̃?, Ṽ) is asymptoticall...

This paper describes a new fractional predator–prey discrete system of the Leslie type. In addition, non-linear dynamics suggested model are examined within framework commensurate and non-commensurate orders, using different numerical techniques such as Lyapunov exponent, phase portraits, bifurcation diagrams. These behaviours imply that type has rich complex dynamical properties influenced by ...

This paper investigates the dynamics of a discrete fractional prey-predator system. The interaction is modelled using square root functional response, which appropriately models systems in prey exhibits strong herd structure, implying that predator generally interacts with along herd's outer corridor. Some recent field experiments and studies show predators affect by directly killing inducing f...

The semi-implicit schemes for the nonlinear predator-prey reactiondiffusion model with the space-time fractional derivatives are discussed, where the space fractional derivative is discretized by the fractional centered difference and WSGD scheme. The stability and convergence of the semi-implicit schemes are analyzed in the L∞ norm. We theoretically prove that the numerical schemes are stable ...

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...