Extinction transition in stochastic population dynamics in a random, convective environment

Abstract

Motivated by modeling the dynamics of a population living in a flowing medium where the environmental factors are random in space, we have studied an asymmetric variant of the one-dimensional contact process, where the quenched random reproduction rates are systematically greater in one direction than in the opposite one. The spatial disorder turns out to be a relevant perturbation but, according to results of Monte Carlo simulations, the behavior of the model at the extinction transition is different from the (infinite randomness) critical behavior of the disordered, symmetric contact process. Depending on the strength $a$ of the asymmetry, the critical population drifts either with a finite velocity or with an asymptotically vanishing velocity as $x(t)\sim t^{\mu (a)}$, where $\mu (a)<1$. Dynamical quantities are non-self-averaging at the extinction transition; the survival probability, for instance, shows multiscaling, i.e. it is characterized by a broad spectrum of effective exponents. For a sufficiently weak asymmetry, a Griffiths phase appears below the extinction transition, where the survival probability decays as a non-universal power of the time while, above the transition, another extended phase emerges, where the front of the population advances anomalously with a diffusion exponent continuously varying with the control parameter.

23 pages, 11 figures, typo corrected

References in corpus (5)

• Critical behavior and Griffiths effects in the disordered contact process
• Weakly disordered absorbing-state phase transitions
• The contact process in heterogeneous and weakly-disordered systems
• Population Dynamics in Spatially Heterogeneous Systems with Drift: the generalized contact process
• Disordered contact process with asymmetric spreading

Cited by in corpus (4)

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• Striated Populations in Disordered Environments with Advection
• Distribution of dynamical quantities in the contact process, random walks, and quantum spin chains in random environments
• Scaling of local persistence in the disordered contact process