In this paper, we consider the following linear Korteweg–de Vries–Benjamin Bona Mahony (KdV-BBM) equation on a finite interval.$ \left\{ \begin{array}{ll} u_t - a^2u_{xxt} + u_x u_{xxx} = 0, & (x, t)\in(0, L)\times (0, \infty), \\ u(0, t) u(L, u_x(L, &t\in u(x, 0) u_0(x), x \in L). \end{array} \right. $We show well-posedness by semigroup theory. A set of critical length $ \mathcal{L} is...

This paper is devoted to studying both the global and local stability of dynamical neural networks. In particular, it has focused on nonlinear neural networks with perturbation. Properties relating to asymptotic and exponential stability and instability have been detailed. This paper also looks at the robustness of neural networks to perturbations and examines if the related properties have bee...

Abstract This paper presents new exponential stability conditions for a class of linear systems with time-varying delay. Unlike the previous works, the delay function considered in this paper is time-varying without any requirement on the derivative, which means that a fast time-varying delay is allowed. Based on an improved Lyapunov-Krasovskii functional combined with Newton-Leibniz formula an...

For a family of non-autonomous differential equations with distributed delays, we give sufficient conditions for the global exponential stability of an equilibrium point. This family includes most of the delayed models of neural networks of Hopfield type, with time-varying coefficients and distributed delays. For these models, we establish sufficient conditions for their global exponential stab...

In this paper, the issue of pth moment exponential stability of stochastic recurrent neural network with distributed time delays is investigated. By using the method of variation parameters, inequality techniques, and stochastic analysis, some sufficient conditions ensuring pth moment exponential stability are obtained. The method used in this paper does not resort to any Lyapunov function, and...

⎯In this paper, global exponential stability of almost periodic solution of cellular neural networks with time-varing delays (CNNVDs) is considered. By using the methods of the topological degree theory and generalized Halanay inequality, a few new applicable criteria are established for the existence and global exponential stability of almost periodic solution. Some previous results are improv...

The problem of global exponential stabilization by boundary feedback for the Korteweg-de Vries-Burgers equation on the domain [0, 1] is considered. We derive a control law of the form u(0) = ux(1) = uxx(1) − k[u(1)3 + u(1)] = 0, where k is a sufficiently large positive constant, and prove that it guarantees L2-global exponential stability, H3-global asymptotic stability, and H3-semiglobal expon...

This paper considers the problem of exponential stability and stabilization of switched linear time-delay systems. The system parameter uncertainties are time-varying and unknown but norm-bounded. The delay in the system states is also time-varying. By using an improved Lyapunov–Krasovskii functional, a switching rule for the exponential stability and stabilization is designed in terms of the s...