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We show that if the Lyapunov exponents associated to a linear equation x′ = A(t)x are equal to the given limits, then this asymptotic behavior can be reproduced by the solutions of the nonlinear equation x′ = A(t)x+ƒ(t,x) for any sufficiently small perturbation ƒ. We consider the linear equation with a very general nonuniform behavior which has different growth rates. [ABSTRACT FROM AUTHOR]

This paper is concerned with traveling waves for temporally delayed, spatially discrete reaction-diffusion equations without quasi-monotonicity. We first establish the existence of non-critical traveling waves (waves with speeds c > c*, where c* is minimal speed). Then by using the weighted energy method with a suitably selected weight function, we prove that all noncritical traveling waves ø(x + ct) (monotone or nonmonotone) are time- asymptotically stable, when the initial perturbations around the wavefronts in a certain weighted Sobolev space are small. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a time periodic and diffusive predator-prey model with disease transmission in the prey. First we consider a SI model when the predator species is absent. By introducing the basic reproduction number for the SI model, we show the sufficient conditions for the persistence and extinction of the disease. When the presence of the predator is taken into account, a number of sufficient conditions for the co-existence of the prey and predator species, the global extinction of predator species and the global extinction of both the prey and predator species are given. [ABSTRACT FROM AUTHOR]

In this work, we analyze the stochastic fractional Ginzburg-Landau equation with multiplicative noise in two spatial dimensions with a particular interest in the asymptotic behavior of its solutions. To get started, we first transfer the stochastic fractional Ginzburg-Landau equation into a random equation whose solutions generate a random dynamical system. The existence of a random attractor for the resulting random dynamical system is explored, and the Hausdorff dimension of the random attractor is estimated. [ABSTRACT FROM AUTHOR]

In this paper, we study a delayed predator-prey model with the Leslie-Gower Holling-type II functional response and harvesting terms. The existence of multiple positive periodic solutions for the system and the permanence of the predator-prey model are obtained by means of the generalized Mawhin coincidence degree theory. [ABSTRACT FROM AUTHOR]

In this paper, under certain parametric conditions we are concerned with the first integrals of the Duffing-van der Pol-type oscillator system, which include the van der Pol oscillator and the damped Duffing oscillator etc as particular cases. After applying the method of differentiable dynamics to analyze the bifurcation set and bifurcations of equilibrium points, we use the Lie symmetry reduction method to find two nontrivial infinitesimal generators and use them to construct canonical variables. Through the inverse transformations we obtain the first integrals of the original oscillator system under the given parametric conditions, and some particular cases such as the damped Duffing equation and the van der Pol oscillator system are included accordingly. [ABSTRACT FROM AUTHOR]

An introduction to the journal is presented which features papers on nonlinear systems and analysis including mathematical modeling, applications in mathematical biology and physics, and simulations.

A preface to the December 2014 issue of the journal "Discrete and Continuous Dynamical Systems Series S" is presented.