A predator’s per capita feeding rate on prey, or its functional response, provides a foundation for predator–prey theory. Since 1959, Holling’s prey-dependent Type II functional response, a model that is a function of prey abundance only, has served as the basis for a large literature on predator–prey theory. We present statistical evidence from 19 predator–prey systems that three predator-depe...

We analyze a class of predator-prey models with BeddingtonDeAngelis type functional response. The models incorporate the mutual interference between predators, which stabilizes predator-prey interactions even when only a linear intrinsic growth rate of the prey population is considered. Positive and elementary stable nonstandard (PESN) finite-difference methods, having the same qualitative feat...

On the basis of the theories and methods of ecology and ordinary differential equation, a seasonally perturbed prey-predator system with the Beddington-DeAngelis functional response is studied analytically and numerically. Mathematical theoretical works have been pursuing the investigation of uniformly persistent, which depicts the threshold expression of some critical parameters. Numerical ana...

This paper is devoted to the existence of periodic solutions for a semi-ratio-dependent predatorprey system with time delays on time scales. With the help of a continuation theorem based on coincidence degree theory, we establish necessary and sufficient conditions for the existence of periodic solutions. Our results show that for the most monotonic prey growth such as the logistic, the Gilpin,...

This paper proposes a secure steganographic communication algorithm based on the evolution of self-organizing patterns. The presented algorithm is a modification of a secure steganographic scheme, presented in our previous work [1]. Algorithm is based on the formation of self-organizing patterns in a Beddington-deAngelis-type predator-prey model with selfdiffusion. Computational experiments sho...

Understanding the effects of fear, quadratic fixed effort harvesting, and predator-dependent refuge are essential topics in ecology. Accordingly, a modified Leslie–Gower prey–predator model incorporating these biological factors is mathematically modeled using Beddington–DeAngelis type functional response to describe predation processes. The model’s qualitative features investigated, including ...

This paper studies the existence and multiplicity of periodic orbits a stage-structured predator-prey model with Beddington-DeAngelis functional response. We derive an criterion orbit in terms inequalities system's nine parameters prove that system admits at least two limit cycles or three via subcritical Hopf bifurcation generalized theory hypersurface theory. also each one-parameter possesses...

In the present paper, we study effect of antipredator behavior due to fear predation on a modified Leslie-Gower predator-prey model incorporating prey refuge which rate predators follows Beddington-DeAngelis functional response. The biological justification is demonstrated through non-negativity, boundedness, and permanence. Next, perform analysis equilibrium local stability. We obtain four poi...