In this paper, a discretized multigroup SIR epidemic model is constructed by applying nonstandard finite difference schemes toa class of continuous time models. This discretization scheme has the same dynamics withthe original differential system independent step, such as positivity solutions and stability equilibria. Discrete-time analogue Lyapunov functions introduced to show that global asymptotic fully determined basic reproductionnumber $R_0$.

A kind of discrete system according to Nicholson′s blowflies equation with a finite delay is obtained by the Euler forward method, and dynamics this are investigated. Applying theory normal form center manifold, we not only discuss linear stability equilibrium existence local Hopf bifurcations, but also give explicit algorithm for determining direction bifurcation periodic solution bifurcation.

This paper is related to the dynamical behaviors of a discrete-time fractional-order predatorprey model. We have investigated existence positive fixed points and parametric conditions for local asymptotic stability this Moreover, it also proved that system undergoes Flip bifurcation Neimark-Sacker point. Various chaos control strategies are implemented controlling due bifurcations. Finally, numerical simulations provided verify theoretical results. These results demonstrate chaotic over...

In this paper, we investigate the global stability of discrete-time coupled systems with multi-diffusion (DCSMDs). By utilizing a multi-digraph theory, construct Lyapunov function for DCSMDs. Consequently, some sufficient conditions are presented to ensure general Then proposed theory is successfully applied analyze predator-prey model which discretized by nonstandard finite difference scheme. Finally, an example numerical simulation given demonstrate effectiveness obtained results.

We study a discrete delay Mosquito population equation. Firstly, we the stability of equilibria system and existence period-two bifurcation by analyzing characteristic Secondly, direction are determined using normal form theory. Finally, some computer simulations performed to illustrate analytical results found.

When an impulsive control is adopted for a stochastic delay difference system (SDDS), there are at least two situations that should be contemplated. If the SDDS stable, then what kind of impulse can original tolerate to keep stable? unstable, strategy taken make Using Lyapunov‐Razumikhin technique, we establish criteria stability equations and these answer those questions. As applications, consider equation present some corollaries our main results.

In this article, we study a discrete delayed flour beetle population equation. Firstly, the existence of period-doubling bifurcation and Neimark–Sacker bifurcations for system by analysing its characteristic equations. Secondly, investigate direction two stability periodic solutions using normal form theory. Finally, some numerical simulations are carried out to support analytical results.

Abstract In this paper, a NonStandard Finite Difference (NSFD) scheme is constructed, which can be used to determine numerical solutions for an epidemic model with vaccination. Here the NSFD method employed derive set of difference equations We show that have same dynamics as original differential system, such positivity and stability equilibria, without being restricted by time step. Our proof global utilizes Lyapunov functions. Numerical simulation illustrates effectiveness our results

This paper considers an impulsive stochastic logistic model with infinite delay at the phase space $C_{g}$. Firstly, definition of solution to functional differential equation is established. Based on this definition, we show that our has a unique global positive solution. Then establish sufficient conditions for extinction, nonpersistence in mean, weak persistence and permanence The threshold between extinction obtained. In addition, effects perturbation are discussed, respectively....

In this article, we investigate the existence and direction of Neimark-Sacker bifurcation equation in title with positive parameters arbitrary non-negative conditions. First, study system by analyzing characteristic equation. Secondly, stability bifurcating invariant curve using normal form theory. Finally, computer simulation is performed to illustrate analytical results found.

This paper is concerned with a stochastic delay logistic model jumps. Sufficient and necessary conditions for extinction are obtained as well permanence. Numerical simulations introduced to support the theoretical analysis results. The results show that jump process can affect properties of population significantly, which conforms biological significance.

Taking white noise into account, a stochastic nonautonomous logistic model is proposed and investigated. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, permanence, global asymptotic stability are established. Moreover, threshold between persistence extinction obtained. Finally, we introduce some numerical simulink graphics to illustrate our main results.

This paper considers a stochastic Gilpin–Ayala model with jumps. First, we show the that has unique global positive solution. Then establish sufficient conditions for extinction, nonpersistence in mean, weak persistence, and permanence of The threshold between persistence extinction is obtained. Finally, make simulations to conform our analytical results. results jump process can change properties population significantly. Copyright © 2014 John Wiley & Sons, Ltd.

In this work, a nonstandard finite difference (NSFD) method is proposed to approximate the solutions of nonlinear reaction–diffusion equation which appears in population dynamics. It well known that model under study has some travelling-wave solutions, are positive, bounded and monotone both space time. First, robust NSFD presented for diffusion-free case original equation. Then, combined with equation, an constructed full shown that, certain conditions on denominator function time-step...

<abstract> In this paper, we propose and investigate an impulsive stochastic predator-prey Lotka-Volterra model with infinite delay Lévy jumps. Sufficient criteria for permanence in time average the threshold between stability extinction are provided. For corresponding case without impulse, easily substantiated sufficient distribution derived. Our results demonstrate that, first of all, coefficients related to have some effects on distribution; then perturbations play a prominent part...

We propose an efficient numerical method for two population models, based on the nonstandard finite difference (NSFD) schemes and composition methods with complex time steps. The NSFD scheme is able to give positive solutions that satisfy conservation law, which a key property biological models. accuracy improved by using Numerical tests plankton nutrient model whooping cough are presented show efficiency advantage of proposed method.