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We consider a couple of models for the dynamics of the populations of two interacting species, inspired by Lotka-Volterra's classical equations. The novelty of this work is that the interaction terms are non local and the interaction occurs…
Dynamical mechanisms that can stabilize the coexistence or diversity in biology are generally of fundamental interest. In contrast to many two-strategy evolutionary games, games with three strategies and cyclic dominance like the…
In this paper we present the simplest individual level model of predator-prey dynamics and show, via direct calculation, that it exhibits cycling behavior. The deterministic analogue of our model, recovered when the number of individuals is…
Many existing studies on pattern formation in the reaction-diffusion systems rely on deterministic models. However, environmental noise is often a major factor which leads to significant changes in the spatiotemporal dynamics. In this…
As a generalization of the 3-strategy Rock-Scissors-Paper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated…
We analyse the stability of linear dynamical systems defined on sparse, random graphs with predator-prey, competitive, and mutualistic interactions. These systems are aimed at modelling the stability of fixed points in large systems defined…
In a two-person Rock-Paper-Scissors (RPS) game, if we set a loss worth nothing and a tie worth 1, and the payoff of winning (the incentive a) as a variable, this game is called as generalized RPS game. The generalized RPS game is a…
The distributions of species lifetimes and species in space are related, since species with good local survival chances have more time to colonize new habitats and species inhabiting large areas have higher chances to survive local…
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…
The classical game of rock-paper-scissors have inspired experiments and spatial model systems that address robustness of biological diversity. In particular the game nicely illustrates that cyclic interactions allow multiple strategies to…
We deal with stochastic network simulations in a model with three distinct species that compete under cyclic rules which are similar to the rules of the popular rock-paper-scissors game. We investigate the Hamming distance density and then…
Cooperation often depends on individuals avoiding exploitation and interacting preferentially with other cooperators. We explore how context-dependent migration influences the evolution of cooperation in spatially structured populations.…
The well-known game of Rock--Paper--Scissors can be used as a simple model of competition between three species. When modelled in continuous time using differential equations, the resulting system contains a heteroclinic cycle between the…
In this paper, we investigate the global boundedness, asymptotic stability and pattern formation of predator-prey systems with density-dependent preytaxis in a two-dimensional bounded domain with Neumann boundary conditions, where the…
Phenotypic plasticity is a key factor in driving the evolution of species in the predator-prey interaction. The natural environment is replete with phenotypic plasticity, which is the source of inducible defences against predators,…
In bio-social models, cooperative behaviour has evolved as an adaptive strategy, playing multi-functional roles. One of such roles in populations is to increase the success of survival and reproduction of individuals and their families or…
We consider the properties of a slow-fast prey-predator system in time and space. We first argue that the simplicity of prey-predator system is apparent rather than real and there are still many of its hidden properties that have been…
Decisions to disperse from a habitat stand out among organismal behaviors as pivotal drivers of ecosystem dynamics across scales. Encounters with other species are an important component of adaptive decision-making in dispersal, resulting…
Stochastic simulations of cyclic three-species spatial predator-prey models are usually performed in square lattices with nearest neighbor interactions starting from random initial conditions. In this Letter we describe the results of…
Standard models of population dynamics focus on the the interaction, survival, and extinction of the competing species individually. Real ecological systems, however, are characterized by an abundance of species (or strategies, in the…