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Analysis of Chaotic Resonance in Izhikevich Neuron Model.

Nobukawa S, Nishimura H, Yamanishi T, Liu JQ - PLoS ONE (2015)

Bottom Line: We found the existence of two distinctive states, a chaotic state involving primarily turbulent movement and an intermittent chaotic state.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Management Information Science, Fukui University of Technology, Fukui, Japan.

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.

No MeSH data available.


Related in: MedlinePlus

Dependence of signal response on signal frequency f0.(a) maxτC(τ). (b) MI(F; S). (c) λj. (a = 0.2, b = 2, c = −56, I = −99, d = −12.19, A = 0.01).
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pone.0138919.g014: Dependence of signal response on signal frequency f0.(a) maxτC(τ). (b) MI(F; S). (c) λj. (a = 0.2, b = 2, c = −56, I = −99, d = −12.19, A = 0.01).

Mentions: Finally, we evaluated the dependence of signal response on signal frequency in CR under the condition A = 0.01, d = −12.19. As shown in Fig 14, the dependence of maxτC(τ) ((a)) and MI(F; S) ((b)) on signal frequency f0 recorded a peak at f0 ≈ 0.103 [kHz] with chaotic state (λ1 > 0 ((c))). Thus, CR has a resonance frequency, as is the case with resonance phenomena in general.


Analysis of Chaotic Resonance in Izhikevich Neuron Model.

Nobukawa S, Nishimura H, Yamanishi T, Liu JQ - PLoS ONE (2015)

Dependence of signal response on signal frequency f0.(a) maxτC(τ). (b) MI(F; S). (c) λj. (a = 0.2, b = 2, c = −56, I = −99, d = −12.19, A = 0.01).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4589341&req=5

pone.0138919.g014: Dependence of signal response on signal frequency f0.(a) maxτC(τ). (b) MI(F; S). (c) λj. (a = 0.2, b = 2, c = −56, I = −99, d = −12.19, A = 0.01).
Mentions: Finally, we evaluated the dependence of signal response on signal frequency in CR under the condition A = 0.01, d = −12.19. As shown in Fig 14, the dependence of maxτC(τ) ((a)) and MI(F; S) ((b)) on signal frequency f0 recorded a peak at f0 ≈ 0.103 [kHz] with chaotic state (λ1 > 0 ((c))). Thus, CR has a resonance frequency, as is the case with resonance phenomena in general.

Bottom Line: We found the existence of two distinctive states, a chaotic state involving primarily turbulent movement and an intermittent chaotic state.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Management Information Science, Fukui University of Technology, Fukui, Japan.

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.

No MeSH data available.


Related in: MedlinePlus