Global stability of bistable traveling wavefronts for a three-species Lotka-Volterra competition system with nonlocal dispersal

This paper is devoted to the study of traveling wavefronts for a three-component Lotka-Volterra system with nonlocal dispersal.This system arises in the study of three-species competition model in which there is no competition between two of these three species.It has been shown that this system admits a bistable traveling wavefront.In this paper,we further investigate the stability of bistable traveling wavefronts.By constructing suitable super-and sub-solutions and using a dynamical system approach,we obtain the globally asymptotic stability of the bistable traveling wavefronts.

STUDY ON THE THREE-SPECIES ALMOST PERIODIC MODEL WITH THE TYPE II FUNCTIONAL RESPONSE

By using Lyapunov function and differential inequality, sufficient conditions for the existence of global asymptotical stable almost periodic solution of the three-species almost periodic modei with the type II functional response are obtained.

Numerical solution of time-fractional three-species food chain model arising in the realm of mathematical ecology

T'his research paper implements the fractional homotopy analysis transform technique to compute the approximate analytical solution of the nonlinear three-species food chain model with time-fractional derivatives.The offered technique is a fantastic blend of homotopy analysis method(HAM)and Laplace transform(LT)operator and has been used fruitfully in the numerical computation of various fractional differential equations(FDEs).This paper involves the fractional derivatives of Caputo style.The numerical solutions of this selected fractional-order food chain model are evaluated by making use of the associated initial conditions.It is revealed by the adopting procedure that the more desirable estimation of the solution can be easily acquired through the calculation of some number of iteration terms only-a fact which authenticates the easiness and soundness of the suggested hybrid scherne.The variations of fractional order of time derivative on the solutions for different specific cases have been depicted through graphical presentations.The outcomes demonstrated through the graphs expound that the adopted scheme is very fantastic and accurate.

Traveling wave solutions for a diffusive three-species intraguild predation model

The aim of this work is to investigate the existence and non-existence of traveling wave solutions for a diffusive three-species intraguild predation model which means that one predator can eat its potential resource competitors. The method of upper-lower solution is implemented to show the existence of traveling wave solutions. In order to simplify the construction of an admissible pair of upper lower solution, the scheme of strictly con- tracting rectangle is applied. Finally, the minimal speed c＊ of traveling wave solutions of the model is characterized. If the wave speed is greater than c＊, we show the exis- tence of traveling wave solutions connecting trivial and positive equilibria by combining the upper and lower solutions with the contracting rectangle. On the other hand, if the wave speed is less than c＊, the non-existence of such solutions is also established. Furthermore, to illustrate our theoretical results, some numerical simulations are performed and biological meanings are interpreted.

Stability, Chaos and Estimation of the Unknown Parameters of Habitat Destruction Model with Prey-Predator-Top Predator

This paper is devoted to study the problem of stability, chaos behavior and parameters estimation of the habitat destruction model with three-species (prey, predator and top-predator). The mathematical formula of the model and its proposed interactions are presented. Some important special solutions of systems are discussed. The stationary states of the model are derived. Local stability conditions for the stationary states are derived. Furthermore, the chaotic behavior of the model is discussed and presented graphically. Using Liapunov stability technique, the dynamic estimators of the unknown probabilities and their updating rules are derived. It is found that, the control laws are non-linear functions of the species densities. Numerical illustrative examples are carried out and presented graphically.

THE VOLTERRA MODEL FOR THREE SPACIES PREDATOR-PREY SYSTEMS IN LOOPS

We consider the three species predator-prey model with the same intrinsic growth rates, where species 3 feeds on species 2, species 2 feeds on species 1, species 1 feeds on species 3. An open question raised by Nishan Krikorian is answered: We obtain the necessary and sufficient conditions for all the orbits to be unbounded. We also obtain the necessary and sufficient conditions for the positive equilibrium to be globally stable. It is shown that there exists a family of neutrally stable periodic orbits, in which we extend Darboux method to three-species models for the first time.