The stochastic nature of predator-prey cycles |
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Authors: | Tânia Tomé Áttila L Rodrigues Mário J de Oliveira |
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Affiliation: | a Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05314-970 São Paulo, SP, Brazil b Departamento de Física, ICEB, Campus Morro do Cruzeiro, Universidade Federal de Ouro Preto, 35400-000 Ouro Preto, Minas Gerais, Brazil |
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Abstract: | We study by numerical simulations the time correlation function of a stochastic lattice model describing the dynamics of coexistence of two interacting biological species that present time cycles in the number of species individuals. Its asymptotic behavior is shown to decrease in time as a sinusoidal exponential function from which we extract the dominant eigenvalue of the evolution operator related to the stochastic dynamics showing that it is complex with the imaginary part being the frequency of the population cycles. The transition from the oscillatory to the nonoscillatory behavior occurs when the asymptotic behavior of the time correlation function becomes a pure exponential, that is, when the real part of the complex eigenvalue equals a real eigenvalue. We also show that the amplitude of the undamped oscillations increases with the square root of the area of the habitat as ordinary random fluctuations. |
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Keywords: | 87 23 Cc 87 10 Hk 05 70 Ln |
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