Related papers: Analysis of Reaction-Diffusion Predator-Prey Syste…
In this paper, we investigate so-called forced wave solutions of a three components reaction-diffusion system from population dynamics. Our system involves three species that are respectively two competing preys and one predator; moreover,…
In biology phenotypic switching is a common bet-hedging strategy in the face of uncertain environmental conditions. Existing mathematical models often focus on periodically changing environments to determine the optimal phenotypic response.…
We propose a novel framework for analyzing the dynamics of distribution shift in real-world systems that captures the feedback loop between learning algorithms and the distributions on which they are deployed. Prior work largely models…
In this paper we investigate the dynamical properties of a spatially periodic reaction-diffusion system {whose reaction terms are of hybrid nature in the sense that they are partly competitive and partly cooperative depending on the value…
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…
We study the stochastic spatial Lotka-Volterra (LV) model for predator-prey interaction subject to a periodically varying carrying capacity. The LV model with on-site lattice occupation restrictions that represent finite food resources for…
The aim of this paper is to study a PDE model for two diffusing species interacting by local size exclusion and global attraction. This leads to a nonlinear degenerate cross-diffusion system, for which we provide a global existence result.…
In this paper, we investigate the emergence of a predator-prey system with Ivlev-type functional response and reaction-diffusion. We study how diffusion affects the stability of predator-prey coexistence equilibrium and derive the…
A delayed, discrete-time, prey-predator model with Allee effects imposed on prey and predator populations is defined, and dynamics of the system is characterized computationally. The parametric conditions for local asymptotic stability of…
Simulation of stochastic spatially-extended systems is a challenging problem. The fundamental quantities in these models are individual entities such as molecules, cells, or animals, which move and react in a random manner. In big systems,…
In this paper, we consider a stochastic ratio-dependent predator-prey model. We firstly prove the existence, uniqueness and positivity of the solutions. Then, the boundedness of moments of population are studied. Finally, we show the…
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…
Cyclic dominant systems, like rock-paper-scissors game, are frequently used to explain biodiversity in nature, where mobility, reproduction and intransitive competition are on stage to provide the coexistence of competitors. A significantly…
Dynamic exploration for a predator-prey bio-system of two species with ratio-dependent functional response is carried out, where the capability to predate in both the stages of the predator, the juvenile and the matured, is taken into…
The introduction of stochasticity into continuous ecological models frequently relies on phenomenological, diagonal diffusion terms that lack a rigorous microscopic basis. We demonstrate that this standard practice fundamentally…
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…
We investigate existence of stationary solutions to an aggregation/diffusion system of PDEs, modelling a two species predator-prey interaction. In the model this interaction is described by non-local potentials that are mutually…
In this paper, we study multi-species stochastic interacting particle systems and their mean-field McKean-Vlasov partial differential equations (PDEs) in non-convex landscapes. We discuss the well-posedness of the multi-species SDE system,…
The statistical properties of an ecosystem composed of species interacting via pairwise, random interactions and deterministic, concentration limiting self-interaction are studied analytically with tools of equilibrium statistical mechanics…
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…