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This paper investigates drive-response robust synchronization of chaotic systems with disturbance, time-varying delay and input saturation via state feedback control. Sufficient conditions for achieving the synchronization of two chaotic systems are derived on the basis of the Lyapunov theory and the linear matrix inequality (LMI) technique, which is not only to guarantee the asymptotic synchronization but also to attenuate the effects of the perturbation on the overall error system to a prescribed level. Finally, an illustrative numerical simulation is also given to demonstrate the effectiveness of the proposed scheme.

This paper focuses on fault detection filter (FDF) design for continuous-time nonlinear Markovian jump systems (NMJSs) with mode-dependent delay and time-varying transition probabilities (TPs). By using a novel Lyapunov-Krasovskii function and based on convex polyhedron technique, a new FDF, as the residual generator, is constructed to guarantee the mean-square exponential stability and a prescribed level of disturbance attenuation for admissible perturbations of NMJSs. Finally, the numerical simulation is carried out to demonstrate the effectiveness of our method.

This work is concerned with the problem for stochastic genetic regulatory networks (GRNs) subject to mixed time delays via passivity control in which mixed time delays consist of leakage, discrete, and distributed delays. The main aim of this paper is constructing a passivity-based criteria under impulsive perturbations such that the proposed GRNs are stochastically stable. Based on the Lyapunov functional method and Jensen’s integral inequality, we obtain a new set of novel passivity based delay-dependent sufficient condition in the form of LMIs, which can be determined via existing numerical software. Finally, we propose numerical simulations to show the efficiency of the proposed method.

This paper is concerned with the robust stability and stabilization for a class of switched discrete-time systems with state parameter uncertainty. Firstly, a new matrix inequality considering uncertainties is introduced and proved. By means of it, a novel sufficient condition for robust stability and stabilization of a class of uncertain switched discrete-time systems is presented. Furthermore, based on the result obtained, the switching law is designed and has been performed well, and some sufficient conditions of robust stability and stabilization have been derived for the uncertain switched discrete-time systems using the Lyapunov stability theorem, block matrix method, and inequality technology. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes.

In the present article a modified decomposition method is implemented to solve systems of partial differential equations of fractional-order derivatives. The derivatives of fractional-order are expressed in terms of Caputo operator. The validity of the proposed method is analyzed through illustrative examples. The solution graphs have shown a close contact between the exact and LADM solutions. It is observed that the solutions of fractional-order problems converge towards the solution of an integer-order problem, which confirmed the reliability of the suggested technique. Due to better accuracy and straightforward implementation, the extension of the present method can be made to solve other fractional-order problems.

In this article, the authors study the existence of positive periodic solutions for a prescribed mean curvature p-Laplacian equation with a singularity of repulsive type and a time-varying delay $$\biggl(\varphi_{p} \biggl(\frac{x'(t)}{\sqrt{1+(x'(t))^{2}}} \biggr) \biggr)'+\beta x'(t)+g \bigl(t, x(t),x \bigl(t-\tau(t) \bigr) \bigr)=p(t), $$ where $g\rightarrow-\infty$ when $x\rightarrow0^{+}$ . The existence of positive periodic solutions conditions is devised by using the coincidence degree theory and some analysis methods. A numerical example demonstrates the validity of the main results.

Two modified exponential time differencing schemes based on the Fourier spectral method are developed to solve the 3-coupled nonlinear fractional Schrödinger equation. We compare the stability of the schemes by plotting their stability regions. The local truncation errors of the time integrators are proved to be fourth-order. Numerical experiments illustrating the solution to the equations with various parameters and the mass conservation results of the numerical methods are carried out.

In this work, we consider two inverse problems for systems of nonlinear differential and differential-difference evolution equations. We propose a new technique for the solution of such inverse problems. We reduce the problem to a system of functional equations by using the given data and then we obtain the solution by the method of Kuczma (Functional Equations in a Single Variable, 1968).

Using p-adic integral, many new convolution identities involving Bernoulli, Euler and Genocchi numbers are given. MSC:11B68, 11S80.