Abstract We develop a first-principles approach to define the communicability between two nodes in time-varying network with memory. The formulation is based on time-fractional Schrödinger equation, where fractional (of Caputo type) derivative accounts for memory of system. Using Hamiltonian tight-binding formalism we propose temporal as product Mittag-Leffer functions adjacency matrices snapsh...

We present an exponential time integrator for the incompressible Navier-Stokes equation based on the exponential block Krylov (EBK) method [2]. The exact solution of the semi-discrete system, given by a discretization of the Navier--Stokes equation in the spatial dimensions, involves the matrix exponential function. So-called exponential integrators are usually directly based on the formal expr...

In this paper, we consider the Korteweg–de Vries equation with time-dependent delay on boundary or internal feedbacks. Under some assumptions delay, weights of feedbacks and length spatial domain, prove exponential stability results, using appropriate Lyapunov functionals. We finish by numerical simulations that illustrate results influence decay rate.

For cellular neural networks with time-varying delays, the problems of determining the exponential stability and estimating the exponential convergence rate are investigated by employing the Lyapunov–Krasovskii functional and linear matrix inequality (LMI) technique. A novel criterion for the stability, which give information on the delay-dependent property, is derived. Two examples are given t...

The robust exponential stability is investigated for a class of uncertain neutral-type neural networks with discrete and distributed time-varying delays. By introducing a new vector Lyapunov-Krasovskii functional, using Jensen integral inequality, free-weighting matrix method and linear matrix inequality techniques, delay-dependent sufficient conditions are obtained for exponential stability of...

This paper discusses the mean-square exponential stability of uncertain neutral linear stochastic systems with interval time-varying delays. A new augmented Lyapunov-Krasovskii functional LKF has been constructed to derive improved delay-dependent robust mean-square exponential stability criteria, which are forms of linear matrix inequalities LMIs . By free-weight matrices method, the usual res...

The global exponential stability problem for a class of switched systems with mixed time delays is investigated in this paper. LMI-based delay-dependent and delay-independent criteria are proposed to guarantee the exponential stability for our considered systems. Razumikhin-like approach and Leibniz-Newton formula are used to find the stability results. Finally, a numerical example is illustrat...

For bidirectional associate memory neural networks with time-varying delays, the problems of determining the exponential stability and estimating the exponential convergence rate are investigated by employing the Lyapunov functional method and linear matrix inequality (LMI) technique. A novel criterion for the stability, which give information on the delay-dependent property, is derived. A nume...