Castro, Tânia Tomé Martins deRodrigues, Áttila LeãesArashiro, EveraldoOliveira, Mário José de2012-11-292012-11-292009CASTRO, T. T. M. de et al. The stochastic nature of predator prey cycles. Computer Physics Communications, v. 180, n. 4, p. 536-539, abr. 2009. Disponível em: <https://www.sciencedirect.com/science/article/pii/S0010465509000198>. Acesso em: 29 nov. 2012.00104655http://www.repositorio.ufop.br/handle/123456789/1876We 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.en-USPopulation dynamicsPredator–prey systemsPopulation cyclesArtigo publicado em periodicoO periódico Computer Physics Communications concede permissão para depósito do artigo no Repositório Institucional da UFOP. Número da licença: 3345930999597.