Related papers: Pattern formation of a predator-prey system with I…
We discuss a diffusively perturbed predator-prey system. Freedman and Wolkowicz showed that the corresponding ODE can have a periodic solution that bifurcates from a homoclinic loop. When the diffusion coefficients are large, this solution…
Cross-diffusion systems play a central role in mathematical modelling, in which density-dependent dispersal and multiscale mechanisms can lead to spatial segregation and diffusion-driven instabilities. In several relevant examples,…
We study a spatial (two-dimensional) Rosenzweig-MacArthur model under the following assumptions: $(1)$ prey movement follows a nonlinear diffusion, $(2)$ preys have a refuge zone (sometimes called "protection zone") where predators cannot…
We employ partial integro-differential equations to model trophic interaction in a spatially extended heterogeneous environment. Compared to classical reaction-diffusion models, this framework allows us to more realistically describe the…
The predator-prey dynamic appertaining to two species is explored, wherein the predator species is structured into different stages. As evidenced from natural documentation, the immature predators possess the potential to predate albeit not…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
In this work we investigate the process of pattern formation in a two dimensional domain for a reaction-diffusion system with nonlinear diffusion terms and the competitive Lotka-Volterra kinetics. The linear stability analysis shows that…
There are various examples of phenotypic plasticity in ecosystems that serve as the basis for a wide range of inducible defences against predation. These strategies include camouflage, burrowing, mimicry, evasive actions, and even…
When two Turing modes interact, i.e., Turing-Turing bifurcation occurs, superposition patterns revealing complex dynamical phenomena appear. In this paper, superposition patterns resulting from Turing-Turing bifurcation are investigated in…
In this paper we consider a model of a nutrient-prey-predator system in a chemostat with general functional responses, using the input concentration of nutrient as the bifurcation parameter. We study the changes in the existence of isolated…
Mathematical modeling and analysis of spatial-temporal population distributions of interacting species have gained significant attention in biology and ecology in recent times. In this work, we investigate a Bazykin-type prey-predator model…
In this paper, we develop a method of analyzing long transient dynamics in a class of predator-prey models with two species of predators competing explicitly for their common prey, where the prey evolves on a faster timescale than the…
Mechanisms of pattern formation---of which the Turing instability is an archetype---constitute an important class of dynamical processes occurring in biological, ecological and chemical systems. Recently, it has been shown that the Turing…
In this paper, dynamical properties and positive steady states of a diffusive predator-prey system with fear effect and Beddington-DeAngelis functional response subject to Neumann boundary conditions are investigated. Dynamical properties…
On a two-dimensional circular domain, we analyze the formation of spatio-temporal patterns for a class of coupled bulk-surface reaction-diffusion models for which a passive diffusion process occurring in the interior bulk domain is linearly…
Mutual interference and prey refuge are important drivers of predator-prey dynamics. The "exponent" or degree of mutual interference has been under much debate in theoretical ecology. In the present work, we investigate the interplay of the…
Numerical continuation is used to compute solution branches in a two-component reaction-diffusion model of Leslie--Gower type. %in the vicinity of a Turing-Hopf interaction. Two regimes are studied in detail. In the first, the homogeneous…
This paper is concerned with existence, non-existence and uniqueness of positive (coexistence) steady states to a predator-prey system with density-dependent dispersal. To overcome the analytical obstacle caused by the cross-diffusion…
In this paper, we consider the dynamics of a predator-prey system of Gause type with cooperative hunting among predators and Holling III functional response. The known work numerically shows that the system exhibits saddle-node and Hopf…
The memory-based diffusion systems have wide applications in practice. Hopf bifurcations are observed from such systems. To meet the demand for computing the normal forms of the Hopf bifurcations of such systems, we develop an effective new…