Math. Model. Nat. Phenom.
Volume 10, Number 6, 2015Nonlocal reaction-diffusion equations
|Page(s)||48 - 60|
|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
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: firstname.lastname@example.org
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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