Related papers: Amplitude dependent frequency, desynchronization, …
We study the role of the noise in the dynamics of two competing species. We consider generalized Lotka-Volterra equations in the presence of a multiplicative noise, which models the interaction between the species and the environment. The…
The stabilizing effects of local enrichment are revisited. Diffusively coupled host-parasitoid and predator-prey metapopulations are shown to admit a stable fixed point, limit cycle or stable torus with a rich bifurcation structure. A…
When biological populations expand into new territory, the evolutionary outcomes can be strongly influenced by genetic drift, the random fluctuations in allele frequencies. Meanwhile, spatial variability in the environment can also…
We investigate cyclic dominance models and their extensions to both network systems and reaction-diffusion frameworks. Using linear stability analysis, we establish the relationship between the stability of synchronized states in network…
The combined influence of oscillatory excitations and multiplicative stochastic perturbations of white noise type on isochronous systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time and…
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…
Spatially extended population dynamics models that incorporate intrinsic noise serve as case studies for the role of fluctuations and correlations in biological systems. Including spatial structure and stochastic noise in predator-prey…
Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. If multiple such networks are coupled together, the question arises whether these rhythms will synchronize. We investigate the impact of…
Common experience suggests that attracting invariant sets in nonlinear dynamical systems are generally stable. Contrary to this intuition, we present a dynamical system, a network of pulse-coupled oscillators, in which \textit{unstable…
Many biological and chemical systems could be modeled by a population of oscillators coupled indirectly via a dynamical environment. Essentially, the environment by which the individual elements communicate is heterogeneous. Nevertheless,…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
Unidirectionally coupled dynamical system is studied by focusing on the input (or boundary) dependence. Due to convective instability, noise at an up-flow is spatially amplified to form an oscillation. The response, given by the down-flow…
Frequency dependent selection and demographic fluctuations play important roles in evolutionary and ecological processes. Under frequency dependent selection, the average fitness of the population may increase or decrease based on…
The dynamics of a two-species community of $N$ competing individuals is considered, with an emphasis on the role of environmental variations that affect coherently the fitness of entire populations. The chance of fixation of a mutant…
First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of…
The dynamics of well-mixed biological populations is usually studied by mean-field methods and weak-noise expansions. Similar methods have been applied also in spatially extended problems, relying on the fact that these populations are…
Biodiversity widely observed in ecological systems is attributed to the dynamical balance among the competing species. The time-varying populations of the interacting species are often captured rather well by a set of deterministic…
The presence of one or more species at some spatial locations but not others is a central matter in ecology. This phenomenon is related to ecological pattern formation. Nonlocal interactions can be considered as one of the mechanisms…
We examine to what extent the tempo and mode of environmental fluctuations matter for the growth of structured populations. The models are switching, linear ordinary differential equations $x'(t)=A(\sigma(\omega t))x(t)$ where…
We investigate the complex spatiotemporal dynamics of an ecological network with species dispersal mediated via a mean-field coupling. The local dynamics of the network are governed by the Truscott--Brindley model, which is an important…