Abstract
A predator-prey model is considered in which prey is limited by the carrying capacity of the environment, and predator growth rate depends on past quantities of prey. Conditions for stability of an equilibrium, and its bifurcation are established taking into account all the parameters.
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Chow, S.-N., White, R. G.: On the transition from supercritical to subcritical Hopf bifurcations. Math. Methods Appl. Sci. 4, 143–163 (1982)
Cushing, J. M.: Integrodifferential equations and delay models in population dynamics. (Lect. Notes Biomath., vol. 20.) Berlin Heidelberg New York: Springer 1977
Dai, L. S.: Nonconstant periodic solutions in predator-prey systems with continuous time delay. Math. Biosci. 53, 149–157 (1981)
Farkas, M.: Stable oscillations in a predator-prey model with time lag. J. Math. Anal. Appl. 102, 175–188 (1984)
Farkas, A., Farkas, M., Kajtár, L.: On Hopf bifurcation in a predator-prey model. In: Differential equations: qualitative theory, pp. 283–290. (Szeged, 1984). Amsterdam New York: North-Holland 1987
Farkas, A., Farkas, M.: Stable oscillations in a more realistic predator-prey model with time lag. (to appear)
Golubitsky, M., Langford, W. F.: Classification and unfoldings of degenerate Hopf bifurcations. J. Differ. Equations 41, 375–415 (1981)
MacDonald, N.: Time delay in prey-predator models, II Bifurcation theory. Math. Biosci. 33, 227–234 (1977)
Rosenzweig, M. L.: Paradox of enrichment: destabilization of exploitation ecosystems in ecological time. Science 171, 385–387 (1971)
Stépán, G.: Great delay in a predator-prey model. Nonlin. Anal. TMA. 10, 913–929 (1986)
Szabó, G.: A remark on Farkas, M.; Stable oscillations in a predator-prey model with time lag. J. Math. Anal. Appl. (to appear)
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Farkas, A., Farkas, M. & Szabó, G. Multiparameter bifurcation diagrams in predator-prey models with time lag. J. Math. Biology 26, 93–103 (1988). https://doi.org/10.1007/BF00280175
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DOI: https://doi.org/10.1007/BF00280175