Related papers: A stochastic analysis of the spatially extended Ma…
Species diversity in ecosystems is often accompanied by the self-organisation of the population into fascinating spatio-temporal patterns. Here, we consider a two-dimensional three-species population model and study the spiralling patterns…
We apply a perturbative Doi--Peliti field-theoretical analysis to the stochastic spatially extended symmetric Rock-Paper-Scissors (RPS) and May--Leonard (ML) models, in which three species compete cyclically. Compared to the two-species…
We study a class of the stochastic May-Leonard models, with three species dominating each other in a cyclic nonhierarchical way, according to the rock-paper-scissors game. We introduce an unevenness in the system, by considering that one of…
The evolution of states of a spatial ecological model is studied. The model describes an infinite population of point entities placed in $\mathbb{R}^d$ which reproduce themselves at distant points (disperse) and die with rate that includes…
We perform dynamical analysis on a stochastic Rosenzweig-MacArthur model driven by {\alpha}-stable L\'evy motion. We analyze the existence of the equilibrium points, and provide a clear illustration of their stability. It is shown that the…
May and Leonard (SIAM J. Appl. Math 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete…
We study reaction-diffusion systems beyond the Markovian approximation to take into account the effect of memory on the formation of spatio-temporal patterns. Using a non-Markovian Brusselator model as a paradigmatic example, we show how to…
Dynamical systems theory provides powerful methods to extract effective macroscopic dynamics from complex systems with slow modes and fast modes. Here we derive and theoretically support a macroscopic, spatially discrete, model for a class…
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…
We introduce a model of long-range interacting particles evolving under a stochastic Monte Carlo dynamics, in which possible increase or decrease in the values of the dynamical variables is accepted with preassigned probabilities. For…
Moving boundary problems allow to model systems with phase transition at an inner boundary. Driven by problems in economics and finance, in particular modeling of limit order books, we consider a stochastic and non-linear extension of the…
Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this…
Environmental enrichment can destabilize predator--prey coexistence through a Hopf bifurcation, yet real ecosystems are finite and intrinsically stochastic. We investigate how mechanistically derived demographic noise shapes near-Hopf…
Many real-world systems exhibit ``noisy'' evolution in time; interpreting their finitely-sampled behavior as arising from continuous-time processes (in the It\^o or Stratonovich sense) has led to significant success in modeling and analysis…
We propose a model based on coupled multiplicative stochastic processes to understand the dynamics of competing species in an ecosystem. This process can be conveniently described by a Fokker-Planck equation. We provide an analytical…
We study the effects of time and space correlations of an external additive colored noise on the steady-state behavior of a Time-Dependent Ginzburg-Landau model. Simulations show the existence of nonequilibrium phase transitions controlled…
In order to better understand the interplay of partnership and competition in population dynamics we study a family of generalized May-Leonard models with $N$ species. These models have a very rich structure, characterized by different…
Self-arrangement of individuals into spatial patterns often accompanies and promotes species diversity in ecological systems. Here, we investigate pattern formation arising from cyclic dominance of three species, operating near a…
We review the mathematical formalism underlying the modelling of stochasticity in biological systems. Beginning with a description of the system in terms of its basic constituents, we derive the mesoscopic equations governing the dynamics…
The influence that intrinsic local density fluctuations can have on solutions of mean-field reaction-diffusion models is investigated numerically by means of the spatial patterns arising from two species that react and diffuse in the…