Nobukawa Sou, Nishimura Haruhiko, Yamanishi Teruya, Liu Jian-Qin
Department of Management Information Science, Fukui University of Technology, Fukui, Japan.
Graduate School of Applied Informatics, University of Hyogo, Kobe, Hyogo, Japan.
PLoS One. 2015 Sep 30;10(9):e0138919. doi: 10.1371/journal.pone.0138919. eCollection 2015.
In stochastic resonance (SR), the presence of noise helps a nonlinear system amplify a weak (sub-threshold) signal. Chaotic resonance (CR) is a phenomenon similar to SR but without stochastic noise, which has been observed in neural systems. However, no study to date has investigated and compared the characteristics and performance of the signal responses of a spiking neural system in some chaotic states in CR. In this paper, we focus on the Izhikevich neuron model, which can reproduce major spike patterns that have been experimentally observed. We examine and classify the chaotic characteristics of this model by using Lyapunov exponents with a saltation matrix and Poincaré section methods in order to address the measurement challenge posed by the state-dependent jump in the resetting process. We found the existence of two distinctive states, a chaotic state involving primarily turbulent movement and an intermittent chaotic state. In order to assess the signal responses of CR in these classified states, we introduced an extended Izhikevich neuron model by considering weak periodic signals, and defined the cycle histogram of neuron spikes as well as the corresponding mutual correlation and information. Through computer simulations, we confirmed that both chaotic states in CR can sensitively respond to weak signals. Moreover, we found that the intermittent chaotic state exhibited a prompter response than the chaotic state with primarily turbulent movement.
在随机共振（SR）中，噪声的存在有助于非线性系统放大微弱（亚阈值）信号。混沌共振（CR）是一种类似于随机共振但没有随机噪声的现象，已在神经系统中被观察到。然而，迄今为止，尚无研究对混沌共振中某些混沌状态下的脉冲神经网络系统的信号响应特性和性能进行研究和比较。在本文中，我们聚焦于Izhikevich神经元模型，该模型能够重现已通过实验观察到的主要脉冲模式。我们使用带有跳跃矩阵的李雅普诺夫指数和庞加莱截面方法来研究和分类该模型的混沌特性，以应对复位过程中状态依赖跳跃带来的测量挑战。我们发现存在两种不同的状态，一种主要涉及湍流运动的混沌状态和一种间歇性混沌状态。为了评估混沌共振在这些分类状态下的信号响应，我们通过考虑微弱周期信号引入了一个扩展的Izhikevich神经元模型，并定义了神经元脉冲的周期直方图以及相应的互相关和信息。通过计算机模拟，我们证实混沌共振中的两种混沌状态都能对微弱信号做出敏感响应。此外，我们发现间歇性混沌状态比主要涉及湍流运动的混沌状态表现出更快的响应。
