Multiple transitions between coherence resonances induced by mixed-mode bursting with complex fast–slow dynamics

Coherence resonance (CR) in neurons, which highlights the beneficial effects of noise, is generally induced from the resting state. In this study, multiple transitions between CR and anti-CR arise from mixed-mode bursting that includes a quiescent state (QS), bursting, and other dynamic behaviors. In addition to beginning from a saddle-node bifurcation and terminating at a limit-point bifurcation, the burst exhibits other special fast–slow dynamics, i.e., shuttling back and forth across the limit-point bifurcation twice to form two clusters of multiple spikes. These clusters are induced by cooperation among three factors: the coexistence of a stable focus and a limit cycle separated by an unstable limit cycle, the weak attraction of the stable focus due to the small negative real parts of its eigenvalues, and the dependence of the slow-variable nullcline on the membrane potential. Weak noise (D) can induce various numbers of clusters, resulting in various interburst intervals (IBIs) and burst durations (BDs). For strong D, the burst begins at a delayed phase and terminates at an advanced phase, resulting in the disappearance of the clusters and shortened IBIs and BDs. With increasing D, the number of clusters increases, decreases, increases, and then decreases, which induces similar changes in the coefficients of variation of the IBIs and BDs, i.e., multiple transitions between CR and anti-CR. The results include the special dynamics of a burst, a novel example of CR, the dynamic mechanism of CRs, and potential functions of synaptic noise in bursting neurons.