Fig. 5

Simulations of the model (22). The figures give the repartition of the population at different instants in time: $t=0$, $t=0.1$, $t=0.5$, $t=0.6$. For each instant, the two plots in the figures represent the same density $q(t,\theta )$ obtained by two different methods: the Monte Carlo method—blue curve, and the finite differences scheme approach for the model (22)—black curve. The initial Gaussian repartition $q_0$ is represented in the upper left plot. The simulations have been obtained for a constant external influence ${\sigma }_0=20$, the potential jump size—$h=5$, the coupling parameter—$J=3$ and the basic current—$I_b=-1$. The last figure shows the repartition at the final time $t=3$, which evidences a convergence toward an equilibrium repartition