Hybrid control strategy of delayed neural networks and its application to sampled-data systems: an impulsive-based bilateral looped-functional approach

Nonlinear Dynamics - In this work, the problem of hybrid control strategy for delayed neural networks is investigated via an impulsive-based bilateral looped-functional (IBBLF) approach. Firstly, a...     

Persistence properties and wave‐breaking criteria for the Geng‐Xue system

Considered herein is a two‐component Novikov equations (called Geng‐Xue system for short) with cubic nonlinearities. The persistence properties and some unique continuation properties of the solutions to the system in weighted L_p spaces are established. Moreover, a wave‐breaking criterion for strong solutions is determined in the lowest Sobolev space by using the localization analysis in the transport equation theory, and we also give a lower bound for the maximal existence time.     

Continuity and analyticity for a cross-coupled Camassa–Holm equation with waltzing peakons and compacton pairs

In this paper, we mainly study the well-posedness in the sense of Hadamard, non-uniform dependence, Hölder continuity and analyticity of the data-to-solution map for a cross-coupled Camassa–Holm equation with waltzing peakons and compacton pairs on both the periodic and the nonperiodic case. Using a Galerkin-type approximation scheme, it is shown that this equation is well-posed in Sobolev spaces \(H^{s} \times H^{s},s>5/2\) in the sense of Hadamard, that is, the data-to-solution mapis continuous. In conjunction with the well-posedness estimate, it is also proved that this dependence is sharp by showing that the solution map is not uniformly continuous. Furthermore, the Hölder continuous in the \(H^r \times H^r\) topology when \(0\le r< s\) with Hölder exponent \(\alpha \) depending on both s and r are shown. Finally, applying generalized Ovsyannikov type theorem and the basic properties of Sobolev-Gevrey spaces, we prove the Gevrey regularity and analyticity of the CCCH system. Moreover, we obtain a lower bound of the lifespan and the continuity of the data-to-solution map     

Permanence,extinction and periodic solutions in a mathematical model of cell populations affected by periodic radiation

A periodic mathematical model of cell populations affected by periodic radiation is presented and studied in this paper. We obtain some sufficient conditions on the permanence and extinction of the system. Furthermore, criteria on the existence and global asymptotic stability of unique positive periodic solutions are established. Some numerical examples are shown to verify our results. A discussion is presented for further study.     

A delay-range-dependent uniformly asymptotic stability criterion for a class of nonlinear singular systems

This paper investigates a class of nonlinear singular systems. Based on the Lyapunov functional method and the free-weighting matrix method, a uniformly asymptotic stability criterion in terms of only one simple linear matrix inequality (LMI) is addressed, which guarantees stability for such time-varying delay systems. This LMI can be easily solved by convex optimization techniques. Two examples are given to illustrate the effectiveness of the proposed main results. All these results are expected to be of use in the study of nonlinear singular systems.     

Incomplete quenching of heat equations with coupled singular logarithms boundary fluxes

This paper deals with quenching phenomena for a heat equations with coupled singular logarithms boundary fluxes. Under appropriate hypotheses, the non-simultaneous quenching of the solution for the system is proved, and the estimates of quenching rates are given. Then we give a natural continuation of the solution (u,v) after the quenching time when the equations occurs non-simultaneous quenching. Moreover, we identify the heat equations verified by the continuation beyond quenching time, i.e., the equations occurs incomplete quenching.     

Mean square stability analysis of impulsive stochastic differential equations with delays

In this article, based on Lyapunov–Krasovskii functional method and stochastic analysis theory, we obtain some new criteria ensuring mean square stability of trivial solution of a class of impulsive stochastic differential equations with delays. As an application, a class of stochastic impulsive neural network with delays has been discussed. One illustrative example has been provided to show the effectiveness of our results.