Stochastic control of spiking activity bump expansion: monotonic and resonant phenomena (Q6550717)

There is a study on noise-induced spatiotemporal dynamics in non-locally coupled bistable spiking oscillators. The investigation is done numerically on two models of oscillators described in the papers of \textit{S. Tsuji} et al. [Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 3, 985--998 (2007; Zbl 1142.37380)] and \textit{V. Semenov} [Phys. Rev. E 95, No. 5, Article ID 052205, 7 p. (2017; \url{doi:10.1103/PhysRevE.95.052205})].\N\NFirstly, a ring of nonlocally coupled Hindmarsh-Rose oscillators with multiplicative noise with the dynamics described by\N\[\N\epsilon\frac{d{x_i}}{dt}=(a+\sqrt{2D}n_i(t))x_i+\frac{{x^3}_i}{3}-y_i+ \frac{\sigma}{2R}\sum_{j=i-R}^{i+R}(x_j-x_i),\N\]\N\[\frac {d{y_i}}{dt}={x_i}^2+bx_i - cy_i\N\]\Nis considered. The investigation is done by choosing appropriate values for parameters and initial conditions and then visualizing and discussing the results. Among other observations on this model and on the dynamics one shows the monotonic impact of noise. In order to study the robustness of the bump activity control one introduces a specific asymmetry modification in the above system and fixes the values of new parameters. The behavior of the system to multiplicative noise, resulting from experiments, are described and results are visualized.