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In this paper, our aim is mathematical analysis and numerical simulation of a prey-predator model to describe the effect of predation between prey and predator with nonlinear functional response. First, we develop results concerning the boundedness, the existence and uniqueness of the solution. Furthermore, the Lyapunov principle and the Routh–Hurwitz criterion are applied to study respectively the local and global stability results. We also establish the Hopf-bifurcation to show the existence of a branch of nontrivial periodic solutions. Finally, numerical simulations have been accomplished to validate our analytical findings. [ABSTRACT FROM AUTHOR]

In this paper, we give some sufficient conditions to guarantee global asymptotic stability of the zero solution of the third-order nonlinear differential equation: x ′ ′ ′ + g( x, x ′ , x ′ ′ ) + f( x, x ′ ) x ′ + h( x) = 0. Two examples are also given to illustrate our results. Copyright © 2013 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper investigates the impacts of state-dependent impulses on the stability of switching Cohen-Grossberg neural networks (CGNN) by means of B-equivalence method. Under certain conditions, the state-dependent impulsive switching systems can be reduced to the fixed-time ones. Furthermore, a stability criterion for the considered CGNN using the proposed comparison system is established. Finally, two numerical examples are provided to illustrate the efficiency of the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a multi-group SEI model with the bilinear incidence and variable susceptibility and infectivity is analyzed. The susceptible individuals are divided into n groups according to their susceptibility, and infected individuals are divided into m groups according to infectivities. Each group of infected individuals has an exposed period. The basic reproduction number is obtained, and globally asymptotic stability of disease-free equilibrium is proved if . If , the disease-free equilibrium is unstable and the endemic equilibrium exists and is unique, which is globally asymptotically stable. Finally, some numerical examples are given to illustrate the above analysis. [Copyright &y& Elsevier]

Abstract: The present paper investigates the global stability and stabilization of switched Boolean network with impulsive effects. By using the semi-tensor product, the algebraic form of the switched Boolean network with impulsive effects is obtained. Then, sufficient and necessary condition is presented for the global stability of the switched Boolean network with impulsive effects. Furthermore, sufficient and necessary conditions are provided for the stabilization of the switched Boolean network with impulsive effects under two types of controls. Finally, examples are presented to illustrate the main results. [Copyright &y& Elsevier]

Abstract: This paper is concerned with the numerical solution of nonlinear functional differential and functional equations. The adaptation of one-leg methods is considered. It is proved that an A-stable one-leg method is globally stable and a strongly A-stable one-leg method is asymptotically stable under suitable conditions. A numerical test is given to confirm the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this work, we propose a conjecture about the stability of the periodic solutions of the Ricker equation with periodic parameters, which goes beyond the existing theory, and for the special case of period-two parameters we analytically show the conjecture is true. For this case we show that the stability region in parameter space obtained from the conjecture is larger than a previously proposed stability region. The period-three case is investigated numerically and similar extensions are realized. This suggests that the current theory cited in this paper, while giving sufficient conditions for stability is far from optimal. [ABSTRACT FROM AUTHOR]