title: Effect of environment fluctuations on pattern formation of single species.
abstract: System-environment interactions are intrinsically nonlinear and dependent on the interplay between many degrees of freedom. The complexity may be even more pronounced when one aims to describe biologically motivated systems. In that case, it is useful to resort to simplified models relying on effective stochastic equations. A natural consideration is to assume that there is a noisy contribution from the environment, such that the parameters that characterize it are not constant but instead fluctuate around their characteristic values. From this perspective, we propose a stochastic generalization of the nonlocal Fisher-KPP equation where, as a first step, environmental fluctuations are Gaussian white noises, both in space and time. We apply analytical and numerical techniques to study how noise affects stability and pattern formation in this context. Particularly, we investigate noise-induced coherence by means of the complementary information provided by the dispersion relation and the structure function.
authors.affiliation: Center of Mathematics, Computation and Cognition, UFABC, São Paulo, Brazil.
authors.forename: L A
authors.initials: LA
authors.lastname: da Silva
authors.affiliation: Department of Physics, PUC-Rio, Rio de Janeiro, Brazil.
authors.forename: E H
authors.initials: EH
authors.lastname: Colombo
authors.affiliation: Department of Physics, PUC-Rio, Rio de Janeiro, Brazil and Institute of Science and Technology for Complex Systems, Rio de Janeiro, Brazil.
authors.forename: C
authors.initials: C
authors.lastname: Anteneodo
mesh_terms: D004777:Environment; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D011157:Population Dynamics; D013269:Stochastic Processes