Finite-time complete periodic synchronization of memristive neural networks with mixed delays.

In this paper we study the oscillatory behavior of a new class of memristor based neural networks with mixed delays and we prove the existence and uniqueness of the periodic solution of the system based on the concept of Filippov solutions of the differential equation with discontinuous right-hand side. In addition, some assumptions are determined to guarantee the globally exponentially stability of the solution. Then, we study the adaptive finite-time complete periodic synchronization problem and by applying Lyapunov-Krasovskii functional approach, a new adaptive controller and adaptive update rule have been developed. A useful finite-time complete synchronization condition is established in terms of linear matrix inequalities. Finally, an illustrative simulation is given to substantiate the main results.

Novel Corona virus disease infection in Tunisia: Mathematical model and the impact of the quarantine strategy.

Corona virus disease (COVID-19) is an extremely serious infection with an extremely high death rate worldwide. In March, the disease was declared a "global pandemic" by the World Health Organization (WHO). Until now, there is no known vaccine or drug, since the unknown things related to the disease are more important than our theoretical and empirical knowledge. However, mathematical modeling and the estimation of the basic number of reproductions can provide clarifications in order to determine the potential and severity of this epidemic and therefore provide essential information to identify the type of measures and interventions to be taken to control the intensity of the spread of the disease. Hence, in this paper, we propose a new deterministic compartmental model based on the clinical progression of the disease, the epidemiological state of the individuals and the intervention for the dynamics of COVID-19 infections. Our approach consists of seven phenotypes: the susceptible humans, exposed humans, infectious humans, the recovered humans, the quarantine population, there recovered-exposed and deceased population. We proved first through mathematical approach the positivity, boundness and existence of a solution to the considered model. We also studied the existence of the disease free equilibrium and corresponding stability. Our work shows, in particular, that the disease will decrease if the number of reproduction R 0 was less than one. Moreover, the impact of the quarantine strategies to reduce the spread of this disease is discussed. The theoretical results are validated by some numerical simulations of the system of the epidemic's differential equations. It should be mentioned that, the error between the considered model and the official data curve is quite small.

Existence and uniqueness of pseudo almost-periodic solutions of recurrent neural networks with time-varying coefficients and mixed delays.

This paper is concerned with the existence and uniqueness of pseudo almost-periodic solutions to recurrent delayed neural networks. Several conditions guaranteeing the existence and uniqueness of such solutions are obtained in a suitable convex domain. Furthermore, several methods are applied to establish sufficient criteria for the globally exponential stability of this system. The approaches are based on constructing suitable Lyapunov functionals and the well-known Banach contraction mapping principle. Moreover, the attractivity and exponential stability of the pseudo almost-periodic solution are also considered for the system. A numerical example is given to illustrate the effectiveness of our results.