Competitive-Cooperative Processes and Stability of Diffusion Systems

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Competitive-Cooperative Processes and Stability of Diffusion Systems

Show simple item record Lakshmikantham, V. en Ladde, G. S. en 2010-06-04T14:35:37Z en 2010-06-04T14:35:37Z en 1978 en
dc.identifier.uri en
dc.description.abstract Very recently, the stability analysis of deterministic [12], random [12,13] competitive-cooperative process has been made in a systematic and unified way. It is well recognized that the probabilistic models in biological [7,9,19,20,30], physical [7,20,21,30], and social [31] sciences are more realistic than the deterministic models. In this paper, we extend the stability analysis of random competitive-cooperative processes [11] to the stability analysis of competitive processes of the diffusion type. The stability results presented includes the stability analysis of multispecies community models [16,17] under white-noise excitations. All our results are in the frame-work of the earlier results [11-13, 16-18]. The paper is organized as follows: The stability analysis of linear, nonlinear and hierarchic competitive-cooperative processes of diffusion type is developed in sections 2, 3 and 4, respectively. Sufficient conditions are given in order to insure the connective stability in probability of the equilibrium state of the systems in a systematic way. Finally, in section 5, the scope of the stability analysis of competitive-cooperative diffusion processes is shown by illustrating several well-known examples of competitive-cooperative diffusion processes in biological, medical, physical, and social sciences, namely, chemical systems, ecosystems, genetic systems, pharamacological systems, physiological systems, economic systems, armament systems, psychological, and social systems. en
dc.language.iso en_US en
dc.publisher University of Texas at Arlington en
dc.relation.ispartofseries Technical Report;89 en
dc.subject Stability analysis en
dc.subject Competitive-cooperative processes en
dc.subject Competitive processes of the diffusion type en
dc.subject Diffusion systems en
dc.subject.lcsh Mathematical models en
dc.subject.lcsh Mathematics Research en
dc.title Competitive-Cooperative Processes and Stability of Diffusion Systems en
dc.type Technical Report en
dc.publisher.department Department of Mathematics en

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