RESUMEN
In this paper, we study the basic problem of a charged particle in a stochastic magnetic field. We consider dichotomous fluctuations of the magnetic field where the sojourn time in one of the two states are distributed according to a given waiting-time distribution either with Poisson or non-Poisson statistics, including as well the case of distributions with diverging mean time between changes of the field, corresponding to an ergodicity breaking condition. We provide analytical and numerical results for all cases evaluating the average and the second moment of the position and velocity of the particle. We show that the field fluctuations induce diffusion of the charge with either normal or anomalous properties, depending on the statistics of the fluctuations, with distinct regimes from those observed, e.g., in standard Continuous-Time Random Walk models.
RESUMEN
In this work we study a non-linear mathematical model based on three different interacting species. We apply our model to Lake Edward ecosystem consisting in hippos, tilapia fishes and human inhabitants. In this case, we estimate the values of the key parameters using actual data and show the reliability of the proposed model as a predictive tool. We also show, via numerical calculations and parameter values that the ecosystem associated to the lake is very far from reaching a stable equilibrium. Through our analysis we provide the conditions for a possible coexistence among the three species.