In this paper we survey the construction of Lyapunov functions (or functional) for various
ecological models which take the form of ODE systems (or Reaction-Diffusion PDE systems) …

Ratio-dependent predator–prey models are favored by many animal ecologists recently as
more suitable ones for predator–prey interactions where predation involves searching …

The stability and bifurcation analysis for a predator–prey system with the nonlinear Michaelis–
Menten type predator harvesting are taken into account. The existence and stability of …

We consider a predator–prey system of Leslie type with generalized Holling type III
functional response p (x)= mx 2 ax 2+ b x+ 1. By allowing b to be negative (b>− 2 a), p (x) is …

The stability of ecological systems is a fundamental concept in ecology, which offers
profound insights into species coexistence, biodiversity, and community persistence. In this …

The recent broad interest on ratio-dependent based predator functional response calls for
detailed qualitative study on ratio-dependent predator-prey differential systems. A first such …

In this paper, we consider a Leslie–Gower predator–prey model with Allee effect on the prey
and a linear functional response. Here the Allee effect impacts the birth rate of the prey …

Stability conditions for functional differential equations can be obtained using Lyapunov
functionals. Lyapunov Functionals and Stability of Stochastic Functional Differential …

A discrete-time prey–predator model with Holling type II is investigated. For this model, the
existence and stability of three fixed points are analyzed. The bifurcation diagrams, phase …

Refuge provides an important mechanism for preserving many ecosystems. Prey refuges
directly benefit prey but also indirectly benefit predators in the long term. In this paper, we …