SELF-REGULATION MECHANISM OF AN ECOSYSTEM IN A NON-GAUSSIAN FLUCTUATION REGIME

We study a dynamical model for an ecological network of many interacti ng species. We consider a Malthus-Verhulst type of self-regulation mec hanism. In the framework of the mean field theory we study the nonline ar relaxation in three different cases: (a) towards the equilibrium st ate, (b) towards the absorbing barrier, (c) at the critical point. We obtain asymptotic behavior in all different cases for the time average of the process. The dynamical behavior of the system, in the limit of infinitely many interacting species, is investigated in the stability and instability conditions and theoretical results are compared with numerical simulations.