In this paper, global exponential stability in Lagrange sense for periodic neural networks with various activation functions is further studied. By constructing appropriate Lyapunov-like functions, we provide easily verifiable criteria for the boundedness and global exponential attractivity of periodic neural networks. These theoretical analysis can narrow the search field of optimization compu...

We propose a modified Leslie-Gower predator-prey model with Holling-type II schemes and a prey refuge. The structure of equilibria and their linearized stability is investigated. By using the iterative technique and further precise analysis, sufficient conditions on the global attractivity of a positive equilibrium are obtained. Our results not only supplement but also improve some existing one...

The notion of geometric homogeneity is extended for differential inclusions. This kind of homogeneity provides the most advanced coordinate-free framework for analysis and synthesis of nonlinear discontinuous systems. The main qualitative properties of continuous homogeneous systems are extended to the discontinuous setting: the equivalence of the global asymptotic stability and the existence o...

In this paper we will consider the nonlinear impulsive delay host–macroparasite model with periodic coefficients. By means of the continuation theorem of coincidence degree, we establish a sufficient condition for the existence of a positive periodic solution M(t) with strictly positive components. Moreover, we establish a sufficient condition for the global attractivity of M(t) and some suffic...

This paper discusses nonlinear discrete-time maps of the form x(k+1) = F (x(k)), focussing on equilibrium points of such maps. Under some circumstances, Lefschetz fixed-point theory can be used to establish the existence of a single locally attractive equilibrium (which is sometimes globally attractive) when a general property of local attractivity is known for any equilibrium. Problems in soci...

The non-autonomous bouncing ball system consists of a point mass m in a constant gravitational field g, which bounces inelastically on a flat vibrating table. The presented Lyapunov-like method is set up for non-autonomous measure differential inclusions and constructs a decreasing step function W above the oscillating Lyapunov function V . Furthermore, it is proven that the attractivity of the...

In this note, we study the general form of some rational recursive sequences. By some modification of the methods and ideas, as well as the transformation from the paper [K. The global attractivity of the rational difference equation y n = y n−k +yn−m 1+y n−k yn−m , Appl. Math. Lett. 20 (2007), 54–58], we give a new proof for the conjectures posed therein.

The concepts of stability attractivity and asymptotic sta bility for systems subject to restrictions of the input values are intro duced and analyzed in terms of Lyapunov functions A comparison with the well known input to state stability property introduced by Sontag is provided We use these concepts in order to derive su cient conditions for global stabilization for triangular and feedforward...

Taking bothwhite noise and colored environmental noise into account, a general stochastic logistic model under regime switching is proposed and studied. Sufficient conditions for extinction, nonpersistence in the mean, weak persistence, stochastic permanence and global attractivity are established. The critical number between weak persistence and extinction is obtained. Moreover, some simulatio...

This paper investigates the dynamics of non-autonomous competitive systems difference equations with asymptotically constant coefficients. We are mainly interested in global attractivity results for such and application to evolutionary population competition models two species.