Transition from Anti-coherence resonance to coherence resonance for mixed-mode oscillations and period-1 firing of nervous system

Abstract

Identification of dynamics of the mixed-mode oscillations (MMOs), which exhibit transition between oscillations with large and small amplitudes, is very important for nonlinear physics. In this paper, the MMOs with transition between subthreshold oscillations and spikes are investigated in a neuron model. In the absence of noise, the MMOs appear between the resting state and period-1 firing with increasing depolarization current. After introducing white noise, coherence resonance (CR) is evoked from the resting state and non-CR is induced from period-1 firing far from the MMOs, which is consistent with the traditional viewpoint. However, an interesting result that a transition from anti-CR to CR is evoked by noise from both the MMOs and the period-1 firing near the MMOs is acquired, which is characterized by the increase, decrease and increase again of the coefficient of variations of interspike intervals (ISIs) with increasing noise intensity. At small noise intensity, more subthreshold oscillations are evoked by noise to reduce the firing frequency, resulting in faster increase of standard deviation (SD) of ISIs than that of mean value of ISIs, which is the cause for the anti-CR. The decrease of SD is faster for middle noise intensity and is lower for strong noise intensity, which is the cause for the CR. The different stochastic responses of MMOs and period-1 firing nearby at different levels of noise insanity are the dynamical mechanism for the transition from anti-CR to CR. Such results present potential functions of the MMOs and period-1 firing on information processing in the nervous system with noise and extend the conditions for the CR and anti-CR phenomena, which enriches the contents of nonlinear dynamics.

On the occurrence of bursting oscillations in the damping Helmholtz–Rayleigh–Duffing oscillator with slow-changing parametrical and external forcings

“…Bursting oscillations, produced by the coupling of distinct timescale effects, behaving in the switching of different oscillations with amplitudes, are common found in many classical nonlinear systems, such as preypredator model [1,2], circuit oscillators [3,4], energy harvesters [5,6] and neurodynamic systems [7,8]. The switching of the system between oscillations of different amplitudes is essentially a transmission process of information exchange, which has been confirmed from the neuronal experiments [9,10].…”

Intermittent bursting oscillations and the bifurcation analysis in an excited Rayleigh-Duffing oscillator

“…Patsios et al [19] introduced a complex mixed-mode oscillation triggered by the jump mechanism rather than the standard canard phenomenon. Liu et al [20] analyzed the mixed-mode oscillations generated by the trajectory moving between the subthreshold vibrations and repetitive spikers. Xu et al [21] qualitatively expounded the generation of chaotic "Homoclinic/fold" bursting and periodic "fold/fold" bursting by utilizing slow/fast decomposition analysis.…”