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Dynamics of nonlinear ecosystems under colored noise disturbances. (English) Zbl 1281.92072
Summary: Stochastic ecosystems of prey-predator type subjected to colored noises with broad-band spectra are investigated. Nonlinear models are considered for two different scenarios: one is the case of possible abundant prey supply and another is the case of possible large predator population. The stochastic averaging procedure is applied to obtain stationary probability solutions of the nonlinear systems. Two types of colored noise are considered: one is the low-pass filtered noise with the spectrum peak at zero frequency, and another is the randomized harmonic process with the spectrum peak at a nonzero frequency. For either type of the noises, the band width reflecting the level of the noise color can be adjusted using a single parameter. The analytical results are substantiated by those obtained from Monte Carlo simulations. It is found that the noise color has significant effects on the stationary state of the system. A narrower band width leads to a less stable system in the sense that the prey and predator populations deviate farther from the equilibrium point of the system without noise disturbances.

MSC:
92D40 Ecology
93C10 Nonlinear systems in control theory
93E03 Stochastic systems in control theory (general)
60H30 Applications of stochastic analysis (to PDEs, etc.)
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