Issue |
Math. Model. Nat. Phenom.
Volume 10, Number 6, 2015
Nonlocal reaction-diffusion equations
|
|
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Page(s) | 48 - 60 | |
DOI | https://doi.org/10.1051/mmnp/201510605 | |
Published online | 02 October 2015 |
Stochastic Path Perturbation Approach Applied to Non–Local Non–Linear Equations in Population Dynamics
1 Santa Fe Institute,
1399 Hyde Park Road,
Santa Fe, New Mexico
87501,
USA
2 Instituto de Investigaciones
Filosóficas, Bulnes
642, 1428
Buenos Aires,
Argentina
3 Universidad San
Sebastián, Lota
2465, Santiago
7500000, Chile
4 Centro Atómico Bariloche, Instituto
Balseiro and CONICET, 8400
Bariloche,
Argentina
⋆ Corresponding author. E-mail: caceres@cab.cnea.gov.ar
We described the first passage time distribution associated to the stochastic evolution from an unstable uniform state to a patterned one (attractor of the system), when the time evolution is given by an integro-differential equation describing a population model. In order to obtain analytical results we used the Stochastic Path Perturbation Approach introducing a minimum coupling approximation into the nonlinear dynamics, and a stochastic multiscale perturbation expansion. We show that the stochastic multiscale perturbation is a necessary tool to handle other problems like: nonlinear instabilities and multiplicative stochastic partial differential equations. A small noise parameter was introduced to define the random escape of the stochastic field. We carried out Monte Carlo simulations in a non-local Fisher like equation, to show the agreement with our theoretical predictions.
Mathematics Subject Classification: 35R9 / 35R60 / 92D25
Key words: non–linear population dynamics / non–local logistic models / Fisher equation / random escape times / first passage time distribution
© EDP Sciences, 2015
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