Multiple coherence resonances evoked from bursting and the underlying bifurcation mechanism

Abstract

Coherence resonance (CR), which is typical nonlinear phenomenon that noise plays construct roles, has been widely investigated in single neurons at resting state instead of bursting behavior when noise free. In the present paper, multiple CRs evoked from bursting instead of resting state and the underlying bifurcation mechanism are studied in a theoretical neuron model composed of fast subsystem and slow variable, which is very important for the bursting neurons receiving strong synaptic noise in the central nervous system. With increasing noise intensity within a range, the bursting period decreases to induce the burst number increases firstly and then becomes irregular, which results in the increase firstly and then decrease in the corresponding peak of the power spectrum of membrane potentials, i.e., CR is evoked from bursting instead of resting state. With further increasing noise intensity, two other peaks exhibit CR phenomenon, one at middle frequency and middle noise intensity and the other at large frequency and strong noise intensity, which shows that multiple CRs are evoked from bursting. Furthermore, the bifurcation mechanism of the latter two resonant peaks is acquired with fast–slow variable dissection method. With increasing the value of slow variable, the fast subsystem exhibits a fold bifurcation of limit cycle and a subcritical Hopf bifurcation to a stable focus, and the imaginary part of the characteristic value of the focus increases, which implies that spikes evoked from the focus exhibit increasing frequency. The trajectory of the deterministic bursting in phase space locates between the two bifurcations and alternates between the coexisting limit cycle and focus of the fast subsystem. With increasing noise intensity, the value of slow variable of the stochastic bursting increases and moves to a range of the focus of the fast subsystem, and the spikes of the stochastic bursting are evoked from the focus by noise. Therefore, the stronger the noise intensity, the larger the value of slow variable, and the higher frequency the spikes, due to the changes of characteristic values, which is the cause that the peaks with middle and high frequency appear at middle and strong noise intensity, respectively. The results of the present paper extend the concept of CR to multiple CRs evoked from bursting, provide the bifurcation mechanism underlying the multiple CRs, and imply multiple chances to utilize noise to enhance information of bursting neurons.