The Effects of Harvesting on the Dynamics of a Leslie–Gower Model

In this paper, we study a Leslie–Gower predator-prey model with harvesting effects. We carry out local bifurcation analysis and stability analysis. Under certain conditions, the model is shown to undergo a supercritical Hopf bifurcation resulting in a stable limit cycle. Numerical simulations are presented to illustrate our theoretic results.

Flip and Neimark–Sacker Bifurcations in a Coupled Logistic Map System

In this paper, we consider a system of strongly coupled logistic maps involving two parameters. We classify and investigate the stability of its fixed points. A local bifurcation analysis of the system using center manifold theory is undertaken and then supported by numerical computations. This reveals the existence of a flip and Neimark–Sacker bifurcations.

Order and Chaos in a Prey-Predator Model Incorporating Refuge, Disease, and Harvesting

In this paper, a mathematical model consisting of a prey-predator system incorporating infectious disease in the prey has been proposed and analyzed. It is assumed that the predator preys upon the nonrefugees prey only according to the modified Holling type-II functional response. There is a harvesting process from the predator. The existence and uniqueness of the solution in addition to their bounded are discussed. The stability analysis of the model around all possible equilibrium points is investigated. The persistence conditions of the system are established. Local bifurcation analysis in view of the Sotomayor theorem is carried out. Numerical simulation has been applied to investigate the global dynamics and specify the effect of varying the parameters. It is observed that the system has a chaotic dynamics.

The Dynamics of A Square Root Prey-Predator Model with Fear

An ecological model consisting of prey-predator system involving the prey’s fear is proposed and studied. It is assumed that the predator species consumed the prey according to prey square root type of functional response. The existence, uniqueness and boundedness of the solution are examined. All the possible equilibrium points are determined. The stability analysis of these points is investigated along with the persistence of the system. The local bifurcation analysis is carried out. Finally, this paper is ended with a numerical simulation to understand the global dynamics of the system.

Singularity: A maple Library for Local Zero Bifurcation Control of Scalar Smooth Maps

Singularity theory is designed for the local bifurcation analysis and control of singular phenomena. The theory has a significant technical computational burden. However, there does not exist any (symbolic) computer library for this purpose. We suitably generalize some powerful tools from algebraic geometry for correct implementation of the results in singularity theory. We provide some required criteria along with rigorous proofs for efficient and cognitive computer implementation. Our results also address permissible truncation degrees in Taylor expansions of smooth bifurcation maps. Accordingly, an end-user friendly maple library, named “singularity,” is developed for an efficient bifurcation analysis and control of real zeros of scalar smooth maps. We have further written a comprehensive user guide for singularity. The main features of our developed maple library are briefly illustrated along with a few examples.