Abstract
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.
Highlights
By virtue of recent developments in brain measurement technology, it is recognized that information is transmitted among neurons according to their firing rate and their spike timing
We examined the chaotic characteristics of the Izhikevich neuron model in detail by using Lyapunov exponents with a saltation matrix and Poincaré section methods, and discovered two distinctive states: a chaotic state with primarily turbulent movement and an intermittent chaotic state
In order to evaluate the signal response of Chaotic resonance (CR) in these classified states, we introduced an extended Izhikevich neuron model by considering a weak periodic signal, and defined a cycle histogram of neuron spikes, and the corresponding mutual correlation and information
Summary
Chaotic resonance (CR) is a phenomenon similar to SR but without stochastic noise, which has been observed in neural systems. 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. We focus on the Izhikevich neuron model, which can reproduce major spike patterns that have been experimentally observed. 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. We found that the intermittent chaotic state exhibited a prompter response than the chaotic state with primarily turbulent movement
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