Abstract
This paper deals with a new method for the stochastic simulation of a system of non-linear partial differential equations describing the dynamics of the spatial distribution of populations in predator-prey relationship.
This method belongs to Monte-Carlo techniques, used in Operation Research. By generation of random numbers, the horizontal distribution of prey and predator concentrations in a turbulent medium is simulated.
Remarkably, it is shown that stochastic fluctuations drive the system very far from equilibrium and induce a temporal dissipative structure as defined by I. Prigogine. One assists to the creation, propagation and annihilation of concentrations waves, and this, independently of initial and boundary conditions. In fact, stochastic fluctuations induce a bifurcation within the predatorprey system which is structurally unstable.
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Dubois, D.M., Monfort, G. (1978). Stochastic simulation of space-time dependent predator-prey models. In: Stoer, J. (eds) Optimization Techniques Part 1. Lecture Notes in Control and Information Sciences, vol 6. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0007258
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DOI: https://doi.org/10.1007/BFb0007258
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