Limits...
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 maxτC(τ) on parameter d and signal strength A.The dotted red line represents the d-threshold of λ1 > 0 (dthr) at each value of signal strength A (a = 0.2, b = 2, c = −56, I = −99, f0 = 0.1).
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4589341&req=5

pone.0138919.g011: Dependence of maxτC(τ) on parameter d and signal strength A.The dotted red line represents the d-threshold of λ1 > 0 (dthr) at each value of signal strength A (a = 0.2, b = 2, c = −56, I = −99, f0 = 0.1).

Mentions: In the section “Fundamental properties of the model,” we observed that the chaotic state with primarily turbulent movement and the intermittent chaotic state coexisted in the region −17 ≲ d ≲ −12. In this section, we examine the sensitivity of signal response in the region of parameter d, including in the two chaotic states. Fig 11 shows the dependence of maxτC(τ) on parameter d, as well as the signal strength A and the d-threshold of λ1 > 0 (dthr; indicated by the dotted red line) at each value of signal strength A. In the range −17 ≲ d ≲ −14, maxτC (τ) ≳ 0.8 (indicated by the black region) was obtained in 0.1 ≲ A ≲ 1. With increasing value of d, the region occupied by A, satisfied by maxτC(τ) ≳ 0.8, expanded to a smaller A in the range −14 ≲ d ≲ −12, where the laminar movement became dominant. In particular, the minimum signal strength A, satisfied by maxτC(τ) ≳ 0.8, attained a value A ≈ 10−3 at −13 ≲ d ≲ dthr (≈ −12). With regard to delay ∣τ∣, the green filled circles in Fig 11 indicate the points with maxτC(τ) > 0.8 and ∣τ∣ < 1.5 [ms]. In the above region (−13 ≲ d ≲ dthr(≈ −12)), these points distributed at the side of dthr. This region included the points attained promptness (∣τ∣ < 1.5 [ms]) in comparison with the other chaotic region, e.g., ∣τ∣ ≈ 2.7 [ms] at d = −16, where the system exhibited primarily turbulent movement (see Fig 6(d)). Moreover, in the periodic state (λ1 ≈ 0) region of d (d > dthr), maxτC(τ) > 0.8 could not be attained in 1 × 10−3 ≲ A ≲ 1.0. Thus, signal response in chaotic states was more sensitive than in the periodic state. In particular, the chaotic states along the boundary between the chaotic and periodic states, called the edge of chaos [19, 36], exhibited the highest sensitivity and the promptest response among all chaotic states. Note that the distribution of points satisfied with the promptness was localized to a small boundary region in the region with high sensitivity.


Analysis of Chaotic Resonance in Izhikevich Neuron Model.

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

Dependence of maxτC(τ) on parameter d and signal strength A.The dotted red line represents the d-threshold of λ1 > 0 (dthr) at each value of signal strength A (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.g011: Dependence of maxτC(τ) on parameter d and signal strength A.The dotted red line represents the d-threshold of λ1 > 0 (dthr) at each value of signal strength A (a = 0.2, b = 2, c = −56, I = −99, f0 = 0.1).
Mentions: In the section “Fundamental properties of the model,” we observed that the chaotic state with primarily turbulent movement and the intermittent chaotic state coexisted in the region −17 ≲ d ≲ −12. In this section, we examine the sensitivity of signal response in the region of parameter d, including in the two chaotic states. Fig 11 shows the dependence of maxτC(τ) on parameter d, as well as the signal strength A and the d-threshold of λ1 > 0 (dthr; indicated by the dotted red line) at each value of signal strength A. In the range −17 ≲ d ≲ −14, maxτC (τ) ≳ 0.8 (indicated by the black region) was obtained in 0.1 ≲ A ≲ 1. With increasing value of d, the region occupied by A, satisfied by maxτC(τ) ≳ 0.8, expanded to a smaller A in the range −14 ≲ d ≲ −12, where the laminar movement became dominant. In particular, the minimum signal strength A, satisfied by maxτC(τ) ≳ 0.8, attained a value A ≈ 10−3 at −13 ≲ d ≲ dthr (≈ −12). With regard to delay ∣τ∣, the green filled circles in Fig 11 indicate the points with maxτC(τ) > 0.8 and ∣τ∣ < 1.5 [ms]. In the above region (−13 ≲ d ≲ dthr(≈ −12)), these points distributed at the side of dthr. This region included the points attained promptness (∣τ∣ < 1.5 [ms]) in comparison with the other chaotic region, e.g., ∣τ∣ ≈ 2.7 [ms] at d = −16, where the system exhibited primarily turbulent movement (see Fig 6(d)). Moreover, in the periodic state (λ1 ≈ 0) region of d (d > dthr), maxτC(τ) > 0.8 could not be attained in 1 × 10−3 ≲ A ≲ 1.0. Thus, signal response in chaotic states was more sensitive than in the periodic state. In particular, the chaotic states along the boundary between the chaotic and periodic states, called the edge of chaos [19, 36], exhibited the highest sensitivity and the promptest response among all chaotic states. Note that the distribution of points satisfied with the promptness was localized to a small boundary region in the region with high sensitivity.

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