Dynamics of the Almost Periodic Discrete Mackey–Glass Model

This paper is concerned with a class of the discrete Mackey–Glass model that describes the process of the production of blood cells. Prior to proceeding to the main results, we prove the boundedness and extinction of its solutions. By means of the contraction mapping principle and under appropriate assumptions, we prove the existence of almost periodic positive solutions. Furthermore and by the implementation of the discrete Lyapunov functional, sufficient conditions are established for the exponential convergence of the almost periodic positive solution. Examples, as well as numerical simulations are illustrated to demonstrate the effectiveness of the theoretical findings of the paper. Our results are new and generalize some previously-reported results in the literature.

Almost periodic solution of Nicholson’s blowflies difference equation with linear harvesting term

This paper is concerned with Nicholson’s blowflies difference model with linear harvesting term. We obtain sufficient conditions for the existence of an almost periodic positive solution by using contraction mapping principle. The exponential convergence of almost periodic positive solution is derived by discrete Lyapunov functional.

Almost Periodic Solution of a Discrete Commensalism System

A nonautonomous discrete two-species Lotka-Volterra commensalism system with delays is considered in this paper. Based on the discrete comparison theorem, the permanence of the system is obtained. Then, by constructing a new discrete Lyapunov functional, a set of sufficient conditions which guarantee the system global attractivity are obtained. If the coefficients are almost periodic, there exists an almost periodic solution and the almost periodic solution is globally attractive.

Stability Analysis of State Saturation 2D Discrete Time-Delay Systems Based on F-M Model

The problem of stability analysis is investigated for a class of state saturation two-dimensional (2D) discrete time-delay systems described by the Fornasini-Marchesini (F-M) model. The delay is allowed to be a bounded time-varying function. By constructing the delay-dependent 2D discrete Lyapunov functional and introducing a nonnegative scalarβ, a sufficient condition is proposed to guarantee the global asymptotic stability of the addressed systems. Subsequently, the criterion is converted into the linear matrix inequalities (LMIs) which can be easily tested by using the standard numerical software. Finally, two numerical examples are given to show the effectiveness of the proposed stability criterion.

Global Robust Exponential Stability of Discrete-Time BAM Neural Networks with Time Varying Delays

In this paper, the global robust exponential stability is discussed for discrete-time bidirectional associative memory (BAM) neural networks with time varying delays. By the linear matrix inequality (LMI) technique and discrete Lyapunov functional combined with inequality techniques, a new global exponential stability criterion of the equilibrium point is obtained for this system. The proposed result is less restrictive, and easier to check in practice. Remarks are made with other previous works to show the superiority of the obtained results, and the simulation example is used to demonstrate the effectiveness of our result.