Krisztina Kiss

On the dynamics of an n-dimensional ratio-dependent predator–prey system with diffusion

Abstract The main concern of this paper is to study the dynamic of an n -dimensional ratio-dependent predator–prey system with diffusion. More concretely, we study the dissipativeness, the persistence of the system and we obtain condition under which the nontrivial equilibrium is globally asymptotically stable.

Qualitative behavior of n-dimensional ratio-dependent predator–prey systems

Abstract This paper deals with the qualitative properties of an n -dimensional autonomous system of differential equations, modeling the general ratio-dependent predator–prey interaction.

Multiple summation inequalities and their application to stability analysis of discrete-time delay systems

Abstract This paper is devoted to stability analysis of discrete-time delay systems based on a set of Lyapunov–Krasovskii functionals. New multiple summation inequalities are derived that involve the famous discrete Jensen׳s and Wirtinger׳s inequalities, as well as the recently presented inequalities for single and double summation in [16] . The present paper aims at showing that the proposed set of sufficient stability conditions can be arranged into a bidirectional hierarchy of LMIs establishing a rigorous theoretical basis for the comparison of conservatism of the investigated methods. Numerical examples illustrate the efficiency of the method.

n-Dimensional ratio-dependent predator–prey systems with diffusion

Abstract This paper deals with a ratio-dependent predator–prey system with diffusion. We will investigate under what conditions Turing stability or instability occurs in higher dimensions.

Stability analysis of linear systems with interval time-varying delays utilizing multiple integral inequalities

This paper is devoted to stability analysis of continuous-time delay systems with interval time-varying delays having known bounds on the delay derivatives. A parameterized family of Lyapunov–Krasovskii functionals involving multiple integral terms is introduced, and novel multiple integral inequalities are utilized to derive sufficient stability condition for systems with time-varying delays. The efficiency of the proposed method is illustrated by numerical examples.

Non-fragile exponential synchronization of delayed complex dynamical networks with transmission delay via sampled-data control

Abstract This paper is devoted to the non-fragile exponential synchronization problem of complex dynamical networks with time-varying coupling delays via sampled-data static output-feedback controller involving a constant signal transmission delay. The dynamics of the nodes contain s quadratically restricted nonlinearities, and the feedback gain is allowed to have norm-bounded time-varying uncertainty. The control design is based on a Lyapunov–Krasovskii functional, which consists of the sum of terms assigned to the individual nodes, i.e., it is constructed without merging the complex dynamical network’s nodes into a single large-scale system. In this way, the proposed design method has substantially reduced computational complexity and improved conservativeness, and guaranties non-fragile exponential stability of the error system. The sufficient stability condition is expressed in terms of linear matrix inequalities that are solvable by standard tools. The efficiency of the proposed method is illustrated by numerical examples.