Related papers: Instability of spatial patterns and its ambiguous …
We study the patterns generated in finite-time sweeps across symmetry-breaking bifurcations in individual-based models. Similar to the well-known Kibble-Zurek scenario of defect formation, large-scale patterns are generated when model…
Environmental stochasticity is known to be a destabilizing factor, increasing abundance fluctuations and extinction rates of populations. However, the stability of a community may benefit from the differential response of species to…
In the present work, we explore the influence of habitat complexity on the activities of prey and predator of a spatio-temporal system by incorporating self diffusion. First we modify the Rosenzweig-MacArthur predator-prey model by…
Field patterns occur in space-time microstructures such that a disturbance propagating along a characteristic line does not evolve into a cascade of disturbances, but rather concentrates on a pattern of characteristic lines. This pattern is…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
Frequency-dependent selection reflects the interaction between different species as they battle for limited resources in their environment. In a stochastic evolutionary game the species relative fitnesses guides the evolutionary dynamics…
Numerical studies of the May-Leonard model for cyclically competing species exhibit spontaneous spatial structures in the form of spirals. It is desirable to obtain a simple coarse-grained evolution equation describing spatio-temporal…
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 consider instabilities of a single mode with finite wavenumber in inversion symmetric spatially one dimensional systems, where the character of the bifurcation changes from sub- to supercritical behaviour. Starting from a general…
Global, population-wide oscillations in models of cyclic dominance may result in the collapse of biodiversity due to the accidental extinction of one species in the loop. Previous research has shown that such oscillations can emerge if the…
We show how highly-diverse ecological communities may display persistent abundance fluctuations, when interacting through resource competition and subjected to migration from a species pool. This turns out to be closely related to the ratio…
We study a spatial predator-prey model in which prey can enter a protection zone (refuge) inaccessible to predators, while predators exhibit directed movement toward prey-rich regions. The directed movement is modeled by a far-sighted…
Strong nonlinear effects combined with diffusive coupling may give rise to unpredictable evolution in spatially extended deterministic dynamical systems even in the presence of a fully negative spectrum of Lyapunov exponents. This regime,…
Understanding the relationship between complexity and stability in large dynamical systems -- such as ecosystems -- remains a key open question in complexity theory which has inspired a rich body of work developed over more than fifty…
The possibility of complicated dynamic behaviour driven by non-linear feedbacks in dynamical systems has revolutionized science in the latter part of the last century. Yet despite examples of complicated frequency dynamics, the possibility…
We study of the formation of pattern-forming fronts in the presence of a rigidly-propagating parameter ramp which is slowly-varying in space. In the context of the prototypical supercritical complex Ginzburg-Landau equation, we show that…
The effect of thermally generated bulk stochastic forces on the statistical growth dynamics of forwards bifurcating propagating macroscopic patterns is compared with the influence of fluctuations at the boundary of a semiinfinite system,…
Understanding how species persist under interacting stressors is a central challenge in ecology. We develop a spatially explicit reaction-diffusion framework to investigate competing species in landscapes shaped by climate variability,…
Ecosystems frequently display the coexistence of diverse species under resource competition, typically resulting in skewed distributions of rarity and abundance. A potential driver of such coexistence is environmental fluctuations that…
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…