The nonlinear mechanisms underlying the various stochastic dynamics evoked from different bursting patterns in a neuronal model. (English) Zbl 1490.92013
Summary: The stochastic dynamics such as coherence resonance (CR) and anti-CR show that noise plays constructive roles in the nervous system, which are always evoked from the resting-state or the nearby coexisting behaviors instead of bursting. In the present paper, various stochastic dynamics are evoked from different bursting patterns and the corresponding nonlinear mechanisms are presented. Anti-CR, transition from CR to anti-CR, and non-CR characterized by the coefficient of variation (CV) of interspike intervals are induced by noise from the “homoclinic/homoclinic” bursting, “fold/big homoclinic” bursting with quiescent state, and “fold/big homoclinic” bursting with subthreshold oscillations, respectively, which are determined by different stochastic transition regularities between the burst/spike and quiescent state/subthreshold oscillations within the stochastic bursting. The more transitions from spike to subthreshold oscillations to form long duration of subthreshold oscillations evoked by noise near a homoclinic orbit bifurcation, noise-induced more transition from quiescent state to spikes prior to a fold bifurcation, and frequent transitions between spikes and quiescent state are the dominant dynamical mechanisms for the anti-CR, CR, and non-CR, respectively. More detailed causes for the three different stochastic dynamics can be acquired through building relationships between the transitions and the different nonlinear dynamics of the fast subsystem such as the bifurcations, coexisting behaviors, attraction domains, and the distance between the trajectory of bursting and the bifurcation point or border between attraction domains. The comprehensive viewpoint and nonlinear mechanism for the various stochastic dynamics of the different bursting patterns extend the occurrence conditions for the CR or anti-CR and presents modulation measures and potential functions of bursting neurons receiving synaptic noise.
MSC:
| 92C20 | Neural biology |
| 34F15 | Resonance phenomena for ordinary differential equations involving randomness |
Software:
XPPAUTReferences:
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