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Environmental Brownian noise suppresses explosions in population dynamics

Author

Listed:
  • Mao, Xuerong
  • Marion, Glenn
  • Renshaw, Eric

Abstract

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 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 probability one that of the associated stochastic differential equation does not.

Suggested Citation

  • Mao, Xuerong & Marion, Glenn & Renshaw, Eric, 2002. "Environmental Brownian noise suppresses explosions in population dynamics," Stochastic Processes and their Applications, Elsevier, vol. 97(1), pages 95-110, January.
    • Handle: RePEc:eee:spapps:v:97:y:2002:i:1:p:95-110
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    References listed on IDEAS

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    1. Ramanan, Kavita & Zeitouni, Ofer, 1999. "The quasi-stationary distribution for small random perturbations of certain one-dimensional maps," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 25-51, November.
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