Environmental Brownian Noise Suppresses Explosions in Population Dynamics

@inproceedings{Mao2001EnvironmentalBN,
  title={Environmental Brownian Noise Suppresses Explosions in Population Dynamics},
  author={Xuerong Mao and Glenn Marion and Eric Renshaw},
  year={2001}
}
Population systems are often subject to environmental noise, and our aim is to show that (surprisingly) the presence of even a tiny amount can suppress a potential population explosion. To prove this intrinsically interesting result, we stochastically perturb the multivariate deterministic system ẋ(t) = f(x(t)) into the Itô form dx(t) = f(x(t))dt + g(x(t))dw(t), and show that although the solution to the original ordinary differential equation may explode to infinity in a finite time, with… CONTINUE READING

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