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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 on parameter d under weak sinusoidal signal.(a) Bifurcation diagram of ui.(b) Lyapunov exponents λj (j = 1, 2). (c) Coefficient of variation for inter-spike interval CV. (a = 0.2, b = 2, c = −56, I = −99, A = 0.3, f0 = 0.1).
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pone.0138919.g007: Dependence of bifurcation on parameter d under weak sinusoidal signal.(a) Bifurcation diagram of ui.(b) Lyapunov exponents λj (j = 1, 2). (c) Coefficient of variation for inter-spike interval CV. (a = 0.2, b = 2, c = −56, I = −99, A = 0.3, f0 = 0.1).

Mentions: This section concerns the response of the system represented by Eq (11). As mentioned in the section “Fundamental properties of the model,” the system featured periodic firing activity in the region (−12 ≲ d ≲ −5) and chaotic activity, which was generated through the intermittent route to chaos, in the region (−17 ≲ d ≲ −12). We now examine the behavior of the system in the Izhikevich neuron model with a weak sinusoidal signal S(t) (A = 0.3). Fig 7 shows the bifurcation diagram of ui ((a)), λj ((b)), and CV ((c)) as a function of d. In the region −17 ≲ d ≲ −12, the behavior of ui exhibited chaotic activity (λ1 > 0). However, as d increased, λ1 and CV decreases; the system was entrained by S(t) (λ1, 2 < 0), and exhibited a period-2 state at −12 ≲ d ≲ −11.5. In the region −11.5 ≲ d ≲ −5, the system exhibited a periodic state (λ1 ≈ 0, λ2 < 0) and ui showed a slight motion when the range of ui was ≈ 1.


Analysis of Chaotic Resonance in Izhikevich Neuron Model.

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

Dependence of bifurcation on parameter d under weak sinusoidal signal.(a) Bifurcation diagram of ui.(b) Lyapunov exponents λj (j = 1, 2). (c) Coefficient of variation for inter-spike interval CV. (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.g007: Dependence of bifurcation on parameter d under weak sinusoidal signal.(a) Bifurcation diagram of ui.(b) Lyapunov exponents λj (j = 1, 2). (c) Coefficient of variation for inter-spike interval CV. (a = 0.2, b = 2, c = −56, I = −99, A = 0.3, f0 = 0.1).
Mentions: This section concerns the response of the system represented by Eq (11). As mentioned in the section “Fundamental properties of the model,” the system featured periodic firing activity in the region (−12 ≲ d ≲ −5) and chaotic activity, which was generated through the intermittent route to chaos, in the region (−17 ≲ d ≲ −12). We now examine the behavior of the system in the Izhikevich neuron model with a weak sinusoidal signal S(t) (A = 0.3). Fig 7 shows the bifurcation diagram of ui ((a)), λj ((b)), and CV ((c)) as a function of d. In the region −17 ≲ d ≲ −12, the behavior of ui exhibited chaotic activity (λ1 > 0). However, as d increased, λ1 and CV decreases; the system was entrained by S(t) (λ1, 2 < 0), and exhibited a period-2 state at −12 ≲ d ≲ −11.5. In the region −11.5 ≲ d ≲ −5, the system exhibited a periodic state (λ1 ≈ 0, λ2 < 0) and ui showed a slight motion when the range of ui was ≈ 1.

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