We consider a spatially nonautonomous discrete sine-Gordon equation with constant forcing and its continuum limit(s) to model a 0-π Josephson junction with an applied bias current. The continuum limits correspond to the strong coupling limit of the discrete system. The nonautonomous character is due to the presence of a discontinuity point, namely, a jump of π in the sine-Gordon phase. The cont...

The aim of this paper is to give characterizations in terms of Lyapunov functions for nonuniform exponential dichotomies of nonautonomous and noninvertible discrete-time systems.

A nonautonomous discrete predator-prey system incorporating a prey refuge and Holling type II functional response is studied in this paper. A set of sufficient conditions which guarantee the persistence and global stability of the system are obtained, respectively. Our results show that if refuge is large enough then predator species will be driven to extinction due to the lack of enough food. ...

We address the problem of constructing numerical integrators for nonholonomic Lagrangian systems that enjoy appropriate discrete versions of the geometric properties of the continuous flow, including the preservation of energy. Building on previous work on time-dependent discrete mechanics, our approach is based on a discrete version of the Lagrange-d’Alembert principle for nonautonomous systems.

The existence of positive periodic solutions of discrete nonautonomous Lotka-Volterra systems with delays is studied by applying the continuation theorem of coincidence degree theory.

This paper deals with the question of existence of periodic solutions of nonautonomous predator–prey dynamical systems with Beddington–DeAngelis functional response. We explore the periodicity of this system on time scales. New sufficient conditions are derived for the existence of periodic solutions. These conditions extend previous results presented in [M. Bohner, M. Fan, J. Zhang, Existence ...

We investigate the asymptotic behavior of nonautonomous discrete dynamical systems governed by the system of difference equations (recursive equations): yj(n+ 1) = Fj(n, y(n)); j = 1, . . . ,k, n = 0,1,2, . . . , where y(n) = (y1(n), . . . , yk(n)) ∈ Rk, y(0) = x, and Fj(n,·) is a mean of k (≥ 2) positive real numbers, that is, a real-valued function satisfying the internality property min(x)≤ ...