Introduction and permanence of species in a diffusive Lotka-Volterra system with time-dependent coefficients

In this paper we explore the possibilities of the network simulation method (NSM) to simulate the behaviour of an ecosystem with three or more interacting species. To check the capabilities of the method we have applied it to a model based on that proposed by [Kmet', T., Holcík J., 1994. The diffusive Lotka-Volterra model as applied to the population dynamics of the German carp and predator and prey species in the Danube river basin. Ecol. Model. 74, 277-285] to explain the population explosion of the German carp in the Lower Danube. The mathematical model of our system is a diffusive Lotka-Volterra model, in which we suppose the birth rate of forage species to be time-dependent. The simplicity of modelling the introduction or extraction of individuals in a very short time is another interesting feature of the NSM, which allows the permanence or extinction of a species to be predicted. It is seen that the actual time that a new species is introduced in an stable oscillatory ecosystem is a determining factor not only as regards the modification of the maximum and minimum density values recorded for the oscillations of other species (or even their disappearance), but also as regards whether the new species manages to remain in the ecosystem. The possibility that NSM will provide information on how densities and flows evolve in the same simulation is used in this paper to know how the ecosystem itself behaves.