Anomalous biennial oscillations in a Fisher equation with a discretized verhulst term
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The dynamics of a biological population governed by a modified Fisher equation is studied by means of Monte Carlo simulations. Reproduction of the population occurs at discrete times, while transport caused by diffusion and conduction takes place on shorter time scales. The discrete reproduction, modeled with a set of coupled logistic maps, exhibits phenomena which are not evident in the usual continuum version of the Fisher equation. Several mechanisms for biennial oscillations of the total population are investigated. One of these shows an ordered coupling between random diffusive motion and the chaotic attractor of the logistic map.
Key WordsLogistic map diffusion Fisher equation chaos oscillations
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- 1.R. A. Fisher,Ann. Eugenics 7:355 (1937).Google Scholar
- 2.J. D. Murray,Mathematical Biology (Springer-Verlag, Berlin, 1989).Google Scholar
- 3.S. Puri, K. R. Elder, and R. C. Desai,Phys. Lett. A 142:357 (1989).Google Scholar
- 4.O. Schonborn, S. Puri, and R. C. Desai,Phys. Rev. E (1994).Google Scholar
- 5.O. Schonborn, R. C. Desai, and D. Stauffer,J. Phys. A 27:L251 (1994).Google Scholar
- 6.W. Horsthempke and R. Lefever,Noise Induced Transitions (Springer-Verlag, Berlin, 1984).Google Scholar
- 7.K. Kaneko,Phys. Rev. Lett. 65:1391 (1990).Google Scholar
- 8.D. Stassinopoulis, G. Huber, and P. Alstrom,Phys. Rev. Lett. 64:3007 (1990).Google Scholar