Competitive-Cooperative Processes and Stability of Diffusion Systems

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Competitive-Cooperative Processes and Stability of Diffusion Systems

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Title: Competitive-Cooperative Processes and Stability of Diffusion Systems
Author: Lakshmikantham, V.; Ladde, G. S.
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.
Date: 1978

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