The paper discusses nonautonomous discrete Lotka–Volterra type n-species competitive systems with pure-delays and feedback controls. New sufficient conditions for which a part of the n-species remains permanent and others is driven to extinction are established by using the method of multiple discrete Lyapunov functionals and introducing new analysis technique. Our results show that the feedbac...

An extension to the nonautonomous case of the energy equation method for proving the existence of attractors for noncompact systems is presented. A suitable generalization of the asymptotic compactness property to the nonautonomous case, termed uniform asymptotic compactness, is given, and conditions on the energy equation associated with an abstract class of equations that assure the uniform a...

The celebrated Takens' embedding theorem concerns an attractor of a dynamical system in Euclidean space appropriate dimension through generic delay-observation map. also establishes topological conjugacy. In this paper, we show how arbitrary sequence can be mapped into another as attractive solution nonautonomous system. Such mapping entails conjugacy and between the spaces. This result is not ...

This paper studies the quadratic optimal control problem for the discrete-time switched linear stochastic system with nonautonomous subsystems perturbed by Gaussian random noises. The goal is to jointly design a deterministic switching sequence and a continuous feedback law to minimize the expectation of a finite-horizon quadratic cost function. Both the value function and the optimal control s...

In this paper we advance the entropy theory of discrete nonautonomous dynamical systems that was initiated by Kolyada and Snoha in 1996. The first part of the paper is devoted to the measure-theoretic entropy theory of general topological systems. We derive several conditions guaranteeing that an initial probability measure, when pushed forward by the system, produces an invariant measure seque...

Although chaotic attractors for autonomous dynamical systems show sensitive dependence on initial conditions, they also typically support a physical or natural measure that characterizes the statistical behavior of almost all conditions near attractor with respect to background such as Lebesgue. In this paper, we identify under which nonautonomous system limits [Formula: see text] an is guarant...

The spectral transformation technique for symmetric RII polynomials is developed. Use of this technique reveals that the nonautonomous discrete modified KdV (nd-mKdV) lattice is directly connected with the RII chain. Hankel determinant solutions to the semi-infinite nd-mKdV lattice are also presented.

Some multiplicity results are obtained for periodic solutions of the nonautonomous superquadratic second-order discrete Hamiltonian systems Duðt 1Þ þ rF ðt; uðtÞÞ 1⁄4 0 8t 2 Z 0096-3 doi:10. q Sup Outsta * Co E-m Plea Com by using critical point theory, especially, a three critical points theorem proposed by Brezis and Nirenberg. 2007 Elsevier Inc. All rights reserved.

Using Mickens nonstandard method, we obtain a discrete family of nonautonomous eco-epidemiological models that include general functions corresponding to the predation infected and uninfected preys. We results on persistence extinction preys assuming bi-dimensional predator–prey subsystem describes dynamics in absence infection satisfies some assumptions. Some examples simulations are undertake...

In this paper, we theoretically prove the existence of periodic solutions for a nonautonomous discrete-time neural networks by using the topological degree theory. Sufficient conditions are also obtained for the existence of an asymptotically stable periodic solution. As a special case, we obtain the existence of a fixed point to the corresponding autonomous discrete-time neural networks which ...