Summary
Sufficient conditions for global stability inn-species Lotka-Volterra systems with diffusion are derived. Both continuous environments with 0-flux boundary conditions and environments consisting of discrete patches are considered.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Auchmuty, J. F. G.: Qualitative effects of diffusion in chemical systems. Manuscript (1977)
Chewning, W. C.: Migratory effects in predator-prey models, Math. Biosci.23, 253–262 (1975)
Conway, E., Smoller, J.: Diffusion and the predator-prey interaction. SIAM J. Appl. Math.33, 673–686 (1977)
Conway, E., Smoller, J.: A comparison theorem for systems of reaction diffusion equations. Comm. Partial Diff. Eq. In press (1978)
Goh, B. S.: Global stability in two species interactions. J. Math. Biology3, 313–318 (1976)
Goh, B. S.: Global stability in many species systems. Amer. Nat.111, 135–143 (1977)
Kuiper, H. J.: Existence and comparison theorems for nonlinear diffusion systems, J. Math. Anal. Appl.60, 166–181 (1977)
Leung, A.: Limiting behavior for a prey-predator model with diffusion and crowding effects. J. Math Biology6, 87–93 (1978)
Levin, S. A.: Dispersion and population interactions. Amer. Nat.108, 207–228 (1974)
Levin, S. A.: Population dynamic models in heterogeneous environments. Ann. Rev. Ecol. Syst.7, 287–310 (1976)
Levin, S. A., Segel, L. A.: An hypothesis to explain the origin of planktonic patchiness. Nature259, 659 (1976)
Rothe, F.: Convergence to the equilibrium state in the Volterra-Lotka diffusion equations. J. Math. Biology3, 319–324 (1976)
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)
Steele, J. H.: Patchiness. Coastal Upwelling and Ecosystems Anal. Newsl.2, 3–7 (1973)
Steele, J. H.: Spatial heterogeneity and population stability. Nature248, 83 (1974a)
Steele, J. H.: Stability of plankton ecosystems. In: Ecological Stability (ed. M. B. Usher, M. H. Williamson), pp. 179–91. London: Chapman & Hall 1974b
Wiens, J. A.: Population responses to patchy environments. Ann. Rev. Ecol. Syst.7, 81–120 (1976)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Hastings, A. Global stability in Lotka-Volterra systems with diffusion. J. Math. Biology 6, 163–168 (1978). https://doi.org/10.1007/BF02450786
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02450786