Related papers: Novel predator-prey model admitting exact analytic…
In the current study, we took into account a model of nonlinear ``predator-prey'' interactions including the ``Allee effect'' on both populations and disease in the predator population. The population as a whole is split into three: the…
Ecosystems with a large number of species are often modelled as Lotka-Volterra dynamical systems built around a large random interaction matrix. Under some known conditions, a global equilibrium exists and is unique. In this article, we…
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…
We consider a stochastic version of the basic predator-prey differential equation model. The model, which contains a parameter \omega which represents the number of individuals for one unit of prey -- If x denotes the quantity of prey in…
In this work we focus on a natural class of population protocols whose dynamics are modelled by the discrete version of Lotka-Volterra equations. In such protocols, when an agent $a$ of type (species) $i$ interacts with an agent $b$ of type…
This paper is devoted to the mathematical analysis of a nonlinear stochastic reaction-diffusion system modeling predator-prey interactions with prey-taxis and noises. Precisely, we detail the proof of the existence of weak martingale…
The population dynamics of predator-prey systems in the presence of patch-specific predators are explored in a setting where the prey population has access to both habitats. The emphasis is in situations where patch-prey abundance drives…
We describe pattern formation in ecological systems using a version of the classical Lotka-Volterra model characterized by a spatial scale which controls the predator-prey interaction range. Analytical and simulational results show that…
This work derives sufficient conditions for the coexistence and exclusion of a stochastic competitive Lotka-Volterra model. The conditions obtained are close to the necessary conditions. In addition, convergence in distribution of positive…
The comprehension of how local interactions arise in global collective behavior is of utmost importance in both biological and physical research. Traditional agent-based models often rely on static rules that fail to capture the dynamic…
Recently, computational modelling became a very important research tool that enables us to study problems that for decades evaded scientific analysis. Evolutionary systems are certainly examples of such problems: they are composed of many…
It is well established that humans decision making and instrumental control uses multiple systems, some which use habitual action selection and some which require deliberate planning. Deliberate planning systems use predictions of…
The dynamics of a local community of competing species with weak immigration from a static regional pool is studied. Implementing the generalized competitive Lotka-Volterra model with demographic noise, a rich dynamics structure with four…
In this paper we introduce a formal method for the derivation of a predator's functional response from a system of fast state transitions of the prey or predator on a time scale during which the total prey and predator densities remain…
Defeat and success of the competitive invasion of a populated area is described with a standard Lotka-Volterra competition model. The resident is adapted to the heterogeneous living conditions, i.e., its motion is modelled as…
In this paper, we consider the almost periodic dynamics of an impulsive multispecies Lotka-Volterra competition system with time delays on time scales. By establishing some comparison theorems of dynamic equations with impulses and delays…
Approximate Bayesian computation (ABC) methods have become increasingly prevalent of late, facilitating as they do the analysis of intractable, or challenging, statistical problems. With the initial focus being primarily on the practical…
A model of population genetics of the Lotka-Volterra type with mutations on a statistical manifold is introduced. Mutations in the model are described by diffusion on a statistical manifold with a generator in the form of a Laplace-Beltrami…
Following the well-extablished mathematical approach to persistence and its recent developments we give a rigorous theoretical explanation to the numerical results obtained for a certain prey-predator model with functional response of…
We consider a stochastic individual based model where each predator searches during a random time and then manipulates its prey or rests. The time distributions may be non-exponential. An age structure allows to describe these interactions…