Numerical study of the influence of recurrent connexions on the signaling in excitable systems: The dynamical effect of noise recycling

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.

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Bifurcations in tri-stable Duffing–Van der Pol oscillator with recycling noise

Zhang

2018

Mod. Phys. Lett. B

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Recycling noise is a kind of more common noise. The nonlinear dynamic system can be controlled by adjusting its parameters. However, so far, the effect of recycling noise on tri-stable dynamic system has not been reported. In this paper, stochastic P-bifurcations in tri-stable Duffing–Van der Pol oscillator induced by additive recycling noise are investigated. Firstly, the stationary probability density function is derived using stochastic averaging method. Then, the general expression of the critical parameter conditions of stochastic P-bifurcation is given by the singularity theory. The stationary probability density of response amplitude in different parameter areas are also shown, which is verified by Monte Carlo numerical simulation. Based on these results, the influence of related parameters of recycling noise and damping coefficient on the stochastic P-bifurcation is studied. The result shows that the critical parameter of bifurcation can be changed by adjusting the delay time and fraction coefficient of the recycling noise. It has also been found that the stationary probability density and stochastic bifurcation show a periodic dependence on the delay time.

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Numerical study of the influence of recurrent connexions on the signaling in excitable systems: The dynamical effect of noise recycling

Cited by 3 publications

References 37 publications

The nonlinear mechanisms underlying the various stochastic dynamics evoked from different bursting patterns in a neuronal model

The nonlinear mechanisms underlying the various stochastic dynamics evoked from different bursting patterns in a neuronal model

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

Bifurcations in tri-stable Duffing–Van der Pol oscillator with recycling noise

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