Abstract
Motivated by an attractive biophysical problem related to revealing the underlying mechanisms of complex oscillatory forms of neural activity, we study a three-dimensional model having the Lukyanov–Shilnikov bifurcation in the parameter region where the system simulates tonic spiking oscillations. We reveal that additive white noise can transit this system from the spiking regime to the bursting. Moreover, it is found that this phenomenon is accompanied by the coherence resonance in generated oscillations and followed by transition to chaos. We investigate these noise-driven effects using both direct numerical simulation method with statistical post-processing of results as well as the theoretical stochastic sensitivity analysis and the methods of confidence domains and Mahalanobis metrics.
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