arXiv subjects
Publications and source records attributed to Krisztina Kiss.
This paper is devoted to the stability analysis of an n species Lotka-Volterra system with discrete and distributed delays. Stochastic perturbations to the parameters of the model are allowed. Sufficient conditions for the almost sure global asymptotic stability of the positive equilibrium are derived in terms of LMIs. The efficiency of the proposed method is illustrated by numerical examples.
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 P.T. Nam, H. Trinh, P.N. Pathirana, Discrete inequalities based on a multiple auxiliary functions and their applications to stability analysis of time-delay systems, Journal of the Franklin Institute, (2015). 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 comparison of conservatism of the investigated methods. Numerical examples illustrate the efficiency of the method.
This paper deals with the stability properties of a closed market, where capital and labour force are acting like a predator-prey system in population-dynamics. The spatial movement of the capital and labour force are taken into account by cross-diffusion effect. First, we are showing two possible ways for modeling this system in only one country's market (applying a simple functional response and a Holling-type ratio-dependent response as well), examining the conditions of their stability properties. We extend the ratio-dependent model into two countries common market where two kind of cross-diffusion effects are present, and find those additional conditions, whose are necessary for the stability of the global common market besides the stability of each countries local markets. Our four-dimensional model highlights that a hectic movement of the capital toward labour force can cause a Turing instability.
This paper deals with ratio-dependent predator-prey systems with delay. We will investigate under what conditions delay cannot cause instability in higher dimension. We give an example when delay causes instability.