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Hastings, Alan

Global stability in Lotka-Volterra systems with diffusion. (English) Zbl 0393.92013

J. Math. Biol. 6, 163-168 (1978).
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Cited in 71 Documents

MSC:

92D25 Population dynamics (general)
35B35 Stability in context of PDEs

Keywords:

Lotka-Volterra Systems; Sufficient Conditions; Global Stability; Reaction Diffusion Equations
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References:

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[3] Conway, E., Smoller, J.: Diffusion and the predator-prey interaction. SIAM J. Appl. Math.33, 673–686 (1977) · Zbl 0368.35021 · doi:10.1137/0133047
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[10] Levin, S. A.: Population dynamic models in heterogeneous environments. Ann. Rev. Ecol. Syst.7, 287–310 (1976) · doi:10.1146/annurev.es.07.110176.001443
[11] Levin, S. A., Segel, L. A.: An hypothesis to explain the origin of planktonic patchiness. Nature259, 659 (1976) · doi:10.1038/259659a0
[12] Rothe, F.: Convergence to the equilibrium state in the Volterra-Lotka diffusion equations. J. Math. Biology3, 319–324 (1976) · Zbl 0355.92013
[13] Segel, L. A., Levin, S. A.: Application of nonlinear stability theory to the study of the effects of diffusion on predator-prey interactions. Topics in Statistical Mechanics and Biophysics: A Memorial to Julius L. Jackson, Proc. AIP Conf.27, 123–152 (1976) · doi:10.1063/1.30356
[14] Steele, J. H.: Patchiness. Coastal Upwelling and Ecosystems Anal. Newsl.2, 3–7 (1973)
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[16] Steele, J. H.: Stability of plankton ecosystems. In: Ecological Stability (ed. M. B. Usher, M. H. Williamson), pp. 179–91. London: Chapman & Hall 1974b
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