Related papers: Invasion patterns in competitive systems
Many technologically useful materials are polycrystals composed of small monocrystalline grains that are separated by grain boundaries of crystallites with different lattice orientations. The energetics and connectivities of the grain…
We study the main properties of the solution of a Fokker-Planck equation characterized by a variable diffusion coefficient and a polynomial superlinear drift, modeling the formation of consensus in a large interacting system of individuals.…
This paper explores a stochastic Gause predator-prey model with bounded or sub-linear functional response. The model, described by a system of stochastic differential equations, captures the influence of stochastic fluctuations on…
In large but finite populations, weak demographic stochasticity due to random birth and death events can lead to population extinction. The process is analogous to the escaping problem of trapped particles under random forces. Methods…
Spatial pattern formation in excitable fluctuating media was researched analytically from the point of view of the order parameters concept. The reaction-diffusion system in external noise is considered as a model of such medium. Stochastic…
Noise, through its interaction with the nonlinearity of the living systems, can give rise to counter-intuitive phenomena such as stochastic resonance, noise-delayed extinction, temporal oscillations, and spatial patterns. In this paper we…
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,…
A general approach to consider spatially extended stochastic systems with correlations between additive and multiplicative noises subject to nonlinear damping is developed. Within modified cumulant expansion method, we derive an effective…
The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…
Many physical, biological or social systems are governed by history-dependent dynamics or are composed of strongly interacting units, showing an extreme diversity of microscopic behaviour. Macroscopically, however, they can be efficiently…
Pathogen-mediated competition, through which an invasive species carrying and transmitting a pathogen can be a superior competitor to a more vulnerable resident species, is one of the principle driving forces influencing biodiversity in…
We analyze ecological systems that are influenced by random environmental fluctuations. We first provide general conditions which ensure that the species coexist and the system converges to a unique invariant probability measure (stationary…
We study the general properties of stochastic two-species models for predator-prey competition and coexistence with Lotka-Volterra type interactions defined on a $d$-dimensional lattice. Introducing spatial degrees of freedom and allowing…
Two mathematical models of macroevolution are studied. These models have population dynamics at the species level, and mutations and extinction of species are also included. The population dynamics are updated by difference equations with…
We characterize a stochastic dynamical system with tempered stable noise, by examining its probability density evolution. This probability density function satisfies a nonlocal Fokker-Planck equation. First, we prove a superposition…
The existence and characterisation of noise-driven bifurcations from the spatially homogeneous stationary states of a nonlinear, non-local Fokker--Planck type partial differential equation describing stochastic neural fields is established.…
Stationary solutions to a Fokker-Planck equation corresponding to a noisy logistic equation with correlated Gaussian white noises are constructed. Stationary distributions exist even if the corresponding deterministic system displays an…
The relaxation towards equilibrium of systems with long range interactions is not yet fully understood. As a step towards such a comprehension, we propose the study of the dynamical equilibrium fluctuations in a model system with long range…
Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such…
Populations interact non-linearly and are influenced by environmental fluctuations. In order to have realistic mathematical models, one needs to take into account that the environmental fluctuations are inherently stochastic. Often,…