Aperiodic stochastic resonance in neural information processing with Gaussian colored noise
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RESEARCH ARTICLE
Aperiodic stochastic resonance in neural information processing with Gaussian colored noise Yanmei Kang1
•
Ruonan Liu1 • Xuerong Mao2
Received: 28 January 2020 / Revised: 22 August 2020 / Accepted: 1 September 2020 Ó Springer Nature B.V. 2020
Abstract The aim of this paper is to explore the phenomenon of aperiodic stochastic resonance in neural systems with colored noise. For nonlinear dynamical systems driven by Gaussian colored noise, we prove that the stochastic sample trajectory can converge to the corresponding deterministic trajectory as noise intensity tends to zero in mean square, under global and local Lipschitz conditions, respectively. Then, following forbidden interval theorem we predict the phenomenon of aperiodic stochastic resonance in bistable and excitable neural systems. Two neuron models are further used to verify the theoretical prediction. Moreover, we disclose the phenomenon of aperiodic stochastic resonance induced by correlation time and this finding suggests that adjusting noise correlation might be a biologically more plausible mechanism in neural signal processing. Keywords Ornstein–Ulenbeck process Local Lipschitz condition Aperiodic stochastic resonance Mutual information
Introduction Dynamical models from cellular level to network and cortical level usually play a necessary role in cognitive neuroscience (Levin and Miller 1996; Wang et al. 2014; De´li et al. 2017; Mizraji and Lin 2017; Song et al. 2019). Due to the random release of neurotransmitter, the stochastic bombing of synaptic inputs and the random opening and closing of ion channels, noise is ubiquitous in neural systems. Various noise-induced non-equilibrium phenomena disclosed in experimental or dynamical models, such as stochastic synchronization (Kim and Lim 2018), noise induced phase transition (Lee et al. 2014) and stochastic integer multiple discharge (Gu and Pan 2015), are helpful in explaining the biophysical mechanisms underlying neural information processing and coding.
& Yanmei Kang [email protected] 1
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an 710049, China
2
Department of Mathematics and Statistics, University of Strathclyde, Livingstone Tower, 26 Richmond Street, Glasgow G1 1XT, Scotland, UK
Stochastic resonance, initially proposed in exploring the periodicity of the continental ice volume in the quaternary era (Benzi et al. 1981), is such an anti-intuitive phenomenon (Gammaitoni et al. 1998; Nakamura and Tateno 2019; Xu et al. 2020; Zhao et al. 2020), where weak coherent signal can be amplified by noise through certain nonlinearity. In general, a suitable external weak signal is prerequisite for stochastic resonance. When the external weak signal is absent or replaced by an intrinsic periodicity, it is referred to as coherence resonance (Guan et al. 2020), which often appears in systems close to Hopf bifurcation. When the external weak signal is not periodic, it is called aperiodic stochastic resonance (
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