Abstract
We consider a single-species dynamical system which is composed of several patches connected by discrete diffusion. Based on recently developed cooperative system theory and the property of a cooperative matrix, we obtain sufficient and necessary conditions for the system with linear diffusion to be extinct and for one with nonlinear diffusion to be globally stable. We also obtain a critical patch number in the system with linear diffusion for the species to go extinct. These results extend some recent known ones for discrete diffusion systems.
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Research partly supported by the Ministry of Education, Science and Culture, Japan, under Grant 01540177
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Lu, Z., Takeuchi, Y. Global asymptotic behavior in single-species discrete diffusion systems. J. Math. Biol. 32, 67–77 (1993). https://doi.org/10.1007/BF00160375
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DOI: https://doi.org/10.1007/BF00160375