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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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Related in: MedlinePlus

Dependence of bifurcation and signal response on parameter d in CR.Under the condition of weaker signals (A = 0.01) than those shown in Figs 7 and 10. (a) Bifurcation diagram of ui. (b) λj. (c) CV.(d) maxτC(τ). (Upper part indicates time delay ∣τ∣). (e) MI(F; S) (a = 0.2, b = 2, c = −56, I = −99, f0 = 0.1).
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pone.0138919.g012: Dependence of bifurcation and signal response on parameter d in CR.Under the condition of weaker signals (A = 0.01) than those shown in Figs 7 and 10. (a) Bifurcation diagram of ui. (b) λj. (c) CV.(d) maxτC(τ). (Upper part indicates time delay ∣τ∣). (e) MI(F; S) (a = 0.2, b = 2, c = −56, I = −99, f0 = 0.1).

Mentions: We show the exact dependence between bifurcation and signal response given a weaker signal (A = 0.01) than the one used in the section “Dependence on parameter d,” which was set at approximately the strength of a signal to be detected almost on the edge of chaos. Fig 12 shows the bifurcation diagrams of ui ((a)), λj (j = 1, 2) ((b)), CV ((c)), maxτC(τ) ((d)), and MI(F; S) ((e)) as functions of d. ui exhibited chaotic and irregular activity (λ1 > 0, CV ≈ 0.5), and periodic movement with slight motion in its range ui ≈ 0.1 in the regions −17 ≲ d ≲ −12 and −12 ≲ d ≲ −5, respectively. The signal response in the region −17 ≲ d ≲ −14, which exhibited the impressive performance (maxτC(τ) ≈ 0.9 and MI(F; S) ≈ 1.7) at A = 0.3 (see Fig 10), degraded such as at maxτC(τ) ≲ 0.7 and MI(F; S)≲ 1. Nonetheless, the signal response at the edge of chaos maintained satisfactory performance (maxτC(τ) ≈ 0.9 at d ≈ −12.19 and MI(F; S) ≈ 1.6 at d ≈ −12.5) and rapidness (∣τ∣ ≈ 0.1 [ms]). Further, Fig 13 shows the relationship between maxτC(τ) and λ1 in the region −13.5 ≤ d ≤ −11 of Fig 12. The red dotted line indicates the mean value of maxτC(τ) in the bin λ1 with window Δλ1 = 0.001. From this result, we see maxτC(τ) recorded a peak (≈ 1.0) at λ1 ≈ 0.04, i.e., we confirmed that signal response in CR has an unimodal maximum with respect to the degree of stability for chaotic orbits.


Analysis of Chaotic Resonance in Izhikevich Neuron Model.

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

Dependence of bifurcation and signal response on parameter d in CR.Under the condition of weaker signals (A = 0.01) than those shown in Figs 7 and 10. (a) Bifurcation diagram of ui. (b) λj. (c) CV.(d) maxτC(τ). (Upper part indicates time delay ∣τ∣). (e) MI(F; S) (a = 0.2, b = 2, c = −56, I = −99, f0 = 0.1).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0138919.g012: Dependence of bifurcation and signal response on parameter d in CR.Under the condition of weaker signals (A = 0.01) than those shown in Figs 7 and 10. (a) Bifurcation diagram of ui. (b) λj. (c) CV.(d) maxτC(τ). (Upper part indicates time delay ∣τ∣). (e) MI(F; S) (a = 0.2, b = 2, c = −56, I = −99, f0 = 0.1).
Mentions: We show the exact dependence between bifurcation and signal response given a weaker signal (A = 0.01) than the one used in the section “Dependence on parameter d,” which was set at approximately the strength of a signal to be detected almost on the edge of chaos. Fig 12 shows the bifurcation diagrams of ui ((a)), λj (j = 1, 2) ((b)), CV ((c)), maxτC(τ) ((d)), and MI(F; S) ((e)) as functions of d. ui exhibited chaotic and irregular activity (λ1 > 0, CV ≈ 0.5), and periodic movement with slight motion in its range ui ≈ 0.1 in the regions −17 ≲ d ≲ −12 and −12 ≲ d ≲ −5, respectively. The signal response in the region −17 ≲ d ≲ −14, which exhibited the impressive performance (maxτC(τ) ≈ 0.9 and MI(F; S) ≈ 1.7) at A = 0.3 (see Fig 10), degraded such as at maxτC(τ) ≲ 0.7 and MI(F; S)≲ 1. Nonetheless, the signal response at the edge of chaos maintained satisfactory performance (maxτC(τ) ≈ 0.9 at d ≈ −12.19 and MI(F; S) ≈ 1.6 at d ≈ −12.5) and rapidness (∣τ∣ ≈ 0.1 [ms]). Further, Fig 13 shows the relationship between maxτC(τ) and λ1 in the region −13.5 ≤ d ≤ −11 of Fig 12. The red dotted line indicates the mean value of maxτC(τ) in the bin λ1 with window Δλ1 = 0.001. From this result, we see maxτC(τ) recorded a peak (≈ 1.0) at λ1 ≈ 0.04, i.e., we confirmed that signal response in CR has an unimodal maximum with respect to the degree of stability for chaotic orbits.

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