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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.

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Dependence of signal response on parameter d in CR.(a) d dependence of maxτC(τ) between cycle histogram  and input signal . The upper part of this figure shows the time delay ∣τ∣, i.e., these values realize the maximum value of C(τ). (b) d dependence of MI(F; S) between cycle histogram  and input signal . (a = 0.2, b = 2, c = −56, I = −99, A = 0.3, f0 = 0.1).
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pone.0138919.g010: Dependence of signal response on parameter d in CR.(a) d dependence of maxτC(τ) between cycle histogram and input signal . The upper part of this figure shows the time delay ∣τ∣, i.e., these values realize the maximum value of C(τ). (b) d dependence of MI(F; S) between cycle histogram and input signal . (a = 0.2, b = 2, c = −56, I = −99, A = 0.3, f0 = 0.1).

Mentions: Furthermore, we evaluated maxτC(τ) and MI(F;S) for the system shown in Fig 10 (a) and (b), respectively. Here, the upper part of the figure (a) shows the value of ∣τ∣ required to realize the maximum value of C(τ). In the region −17 ≲ d ≲ −13, where the system exhibited chaotic activity, the value of maxτC(τ) increased (≈ 0.9) with the time delay ∣τ∣ ≈ 3 [ms]. Thus, chaotic resonance (CR) arose in this region. As with maxτC(τ), MI(F; S) also maintained a high value (≳ 1.8) in the region (−17 ≲ d ≲ −13), as shown in Fig 10 (b).


Analysis of Chaotic Resonance in Izhikevich Neuron Model.

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

Dependence of signal response on parameter d in CR.(a) d dependence of maxτC(τ) between cycle histogram  and input signal . The upper part of this figure shows the time delay ∣τ∣, i.e., these values realize the maximum value of C(τ). (b) d dependence of MI(F; S) between cycle histogram  and input signal . (a = 0.2, b = 2, c = −56, I = −99, A = 0.3, f0 = 0.1).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0138919.g010: Dependence of signal response on parameter d in CR.(a) d dependence of maxτC(τ) between cycle histogram and input signal . The upper part of this figure shows the time delay ∣τ∣, i.e., these values realize the maximum value of C(τ). (b) d dependence of MI(F; S) between cycle histogram and input signal . (a = 0.2, b = 2, c = −56, I = −99, A = 0.3, f0 = 0.1).
Mentions: Furthermore, we evaluated maxτC(τ) and MI(F;S) for the system shown in Fig 10 (a) and (b), respectively. Here, the upper part of the figure (a) shows the value of ∣τ∣ required to realize the maximum value of C(τ). In the region −17 ≲ d ≲ −13, where the system exhibited chaotic activity, the value of maxτC(τ) increased (≈ 0.9) with the time delay ∣τ∣ ≈ 3 [ms]. Thus, chaotic resonance (CR) arose in this region. As with maxτC(τ), MI(F; S) also maintained a high value (≳ 1.8) in the region (−17 ≲ d ≲ −13), as shown in Fig 10 (b).

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