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A Predator-Prey Model from Collective Dynamics and Self-Propelled Particles Approach.
1  Universit√© Assane Seck de Ziguinchor (Senegal)
Academic Editor: Marjan Mernik

Abstract:

The definition and description of the dynamics of predator-prey system consists in one of the
fundamental problems of the population biology. Since 1925, several models have been introduced.
Although they are highly effective, most of them neglect certain relevant criteria such as the spatial
and temporal distribution of the studied species. It is with the aim of introducing these criteria that
we conduct our study by coupling two models designed intitially for collective dynamics. The first
is for predators mobility, a Vicsek type model ; The second is a Brownian Particle (BP) model for
prey. We observed, as naturally in the classical models, periodic cycles of the density of predators
and prey. In this case, the period of oscillations depends relatively on the collective dynamics
parameters.

Keywords: Collective Behaviour , Self-Propelled Particles, Brownian Particles, Predator-Prey, Reaction- Diffusion, limite Cycle
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