Related papers: Pattern formation in a predator-prey system charac…
Multispecies ecosystems modelled by generalized Lotka-Volterra equations exhibit stationary population abundances, where large number of species often coexist. Understanding the precise conditions under which this is at all feasible and…
To understand the spreading and interaction of prey and predator, in this paper we study the dynamics of the diffusive Lotka-Volterra type prey-predator model with different free boundaries. These two free boundaries, which may intersect…
In this research, we revisit the paper by Pal et al. [Int. J. Appl. Comput. Math (2017) 3:1833-1845] and comment on the claim that global stability of the interior equilibrium point depends on some key parameters. This is not true, and we…
Systems of dynamical interactions between competing species can be used to model many complex systems, and can be mathematically described by {\em random} networks. Understanding how patterns of activity arise in such systems is important…
In this paper, we investigate the emergence of a predator-prey model with Beddington-DeAngelis-type functional response and reaction-diffusion. We derive the conditions for Hopf and Turing bifurcation on the spatial domain. Based on the…
We study the dynamics of a ring of patches with vegetation-prey-predator populations, coupled through interactions of the Lotka-Volterra type. We find that the system yields aperiodic, recurrent and rare explosive bursts of predator density…
Mathematical modelling and numerical simulations of interaction populations are crucial topics in systems biology. The interactions of ecological models may occur among individuals of the same species or individuals of different species.…
We propose a model for the dynamics of frequencies of a costly defense trait. More precisely, we consider Lotka-Volterra-type models involving a prey (or host) population consisting of two types and a predator (or parasite) population,…
Ecology and evolution are inseparable. Motivated by some recent experiments, we have developed models of evolutionary ecology from the perspective of dynamic networks. In these models, in addition to the intra-node dynamics, which…
We study a six-species Lotka-Volterra type system on different two-dimensional lattices when each species has two superior and two inferior partners. The invasion rates from predator sites to a randomly chosen neighboring prey's site depend…
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…
Spatio-temporal complexity of ecological dynamics has been a major focus of research for a few decades. Pattern formation, chaos, regime shifts and long transients are frequently observed in field data but specific factors and mechanisms…
We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one…
Does an ecological community allow stable coexistence? Identifying the general principles that determine the answer to this question is a central problem of theoretical ecology. Random matrix theory approaches have uncovered the general…
Ecological systems show a variety of characteristic patterns of biodiversity in space and time. It is a challenge for theory to find models that can reproduce and explain the observed patterns. Since the advent of island biogeography these…
We analyze a spatially extended version of a well-known model of forest-savanna dynamics, which presents as a system of nonlinear partial integro-differential equations, and study necessary conditions for pattern-forming bifurcations.…
In this work we investigate the development of stable dynamical structures along interfaces separating domains belonging to enemy partnerships, in the context of cyclic predator-prey models with an even number of species $N \ge 8$. We use…
In this work we consider three species competing with each other in the same habitat. One of the species lives in the entire habitat, competing with the other two species, while the other two inhabit two disjoint regions of the habitat.…
The assembly and persistence of ecological communities can be understood as the result of the interaction and migration of species. Here we study a single community subject to migration from a species pool in which inter-specific…
The ecological invasion problem in which a weaker exotic species invades an ecosystem inhabited by two strongly competing native species is modelled by a three-species competition-diffusion system. It is known that for a certain range of…