Stochastic analysis of a pulse-type prey-predator model.
A stochastic Lotka-Volterra model, a so-called pulse-type model, for the interaction between two species and their random natural environment is investigated. The effect of a random environment is modeled as random pulse trains in the birth rate of the prey and the death rate of the predator. The generalized cell mapping method is applied to calculate the probability distributions of the species populations at a state of statistical quasistationarity. The time evolution of the population densities is studied, and the probability of the near extinction time, from an initial state to a critical state, is obtained. The effects on the ecosystem behaviors of the prey self-competition term and of the pulse mean arrival rate are also discussed. Our results indicate that the proposed pulse-type model shows obviously distinguishable characteristics from a Gaussian-type model, and may confer a significant advantage for modeling the prey-predator system under discrete environmental fluctuations.
Wu
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Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou, People's Republic of China.
Zhu
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D000818:Animals; D005075:Biological Evolution; D001723:Birth Rate; D003198:Computer Simulation; D017753:Ecosystem; D004777:Environment; D008954:Models, Biological; D009010:Monte Carlo Method; D011157:Population Dynamics; D011235:Predatory Behavior; D011336:Probability; D015203:Reproducibility of Results; D013037:Spatial Behavior; D013269:Stochastic Processes; D016019:Survival Analysis; D013997:Time Factors