We study the effects of a disease affecting a predator on the dynamics of a predator-prey system. We couple an SIRS model applied to the predator population, to a Lotka-Volterra model. The SIRS model describes the spread of the disease in a predator population subdivided into susceptible, infected and removed individuals. The Lotka-Volterra model describes the predator-prey interactions. We con...

This work investigated the stability of some Lotka-Volterra type models. We used the Liapunov method, which consists in analyzing the stability of systems of ordinary differential equations (ODE's), around the equilibrium, when submitted to perturbations in the initial conditions.

Themodelling of predator–prey dynamics is of great importance in ecology. Models based on differential equations aim to understand the interactions between populations of prey and predators at population scale, but they are unable to handle spatial and individual behaviour heterogeneities (individual scale). In this study, a population-driven individual-based model is proposed that has been dev...

The Leslie-Gower model is a discrete time analog of the competition Lotka-Volterra model and is known to possess the same dynamic scenarios of that famous model. The Leslie-Gower model played a historically significant role in the history of competition theory in its application to classic laboratory experiments of two competing species of flour beetles (carried out by Park in the 1940s-1960s)....

Markov models are widely used to describe the dynamics of communities of sessile organisms, because they are easily fitted to field data and provide a rich set of analytical tools. In typical ecological applications, at any point in time, each point in space is in one of a finite set of states (e.g., species, empty space). The models aim to describe the probabilities of transitions between stat...

In this paper, a model composed of two Lotka-Volterra patches is considered. The system consists of two competing species X, Y and only species Y can diffuse between patches. It is proved that the system has at most two positive equilibria and then that permanence implies global stability. Furthermore, to answer the question whether the refuge is effective to protect Y , the properties of posit...

The main purpose of this article is considering whether or not the feedback controls have an influence on a non-autonomous predator–prey Lotka–Volterra type system. General criteria on permanence are established, which is described by an integral form and independent of some feedback controls. By constructing suitable Lyapunov functionals, a set of easily verifiable sufficient conditions are de...

The noise-induced pattern formation in a population dynamical model of three interacting species in the coexistence regime is investigated. A coupled map lattice of Lotka-Volterra equations in the presence of multi-plicative noise is used to analyze the spatiotemporal evolution. The spatial correlation of the species concentration as a function of time and of the noise intensity is investigated...