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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 spike timing on signal strength A in periodic state.(a) Mean of inter spike interval < Tk >. (b) Spike timing  against input signal. (a = 0.2, b = 2, c = −56, d = −10, I = −99, f0 = 0.1).
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pone.0138919.g009: Dependence of spike timing on signal strength A in periodic state.(a) Mean of inter spike interval < Tk >. (b) Spike timing against input signal. (a = 0.2, b = 2, c = −56, d = −10, I = −99, f0 = 0.1).

Mentions: Fig 8 shows the time series of v(t) (bottom) and the corresponding cycle histogram of the firing counts (top). In case d = −16 ((a)), the neuron fired non-periodically and the cycle histogram responded to the signal with some delay ∣τ∣ ≈ 3[ms]. However, when we changed the value of d to the periodic region, as shown in d = −10 ((b)), the neuron fired periodically and the cycle histogram did not respond to signal . Added to this, we investigated the signal response in the periodic region in detail. Fig 9 indicates < Tk > ((a)) and distribution of ((b)) as a function of A in case d = −10. In 1 × 10−3 ≲ A ≲ 2 × 10−2, < Tk > kept about 8.7 [ms] as a period of autonomous spiking (dashed line) and spread over entire area (−5 to 5 [ms]) uniformly. However, < Tk > began to converge to 10(= T0) [ms] with increasing A in 2 × 10−2 ≲ A ≲ 1. In this region, tended to gather at the specific points by the interaction effect of S(t). Here, the signal amplitude (A = 0.3) used in Fig 8 belonged to this region. In cases of higher signal strength (1 ≲ A ≲ 3), < Tk > and were locked at 10(= T0) [ms] and some specific point within −3.5 ≲ ≲ −1.5 [ms], respectively.


Analysis of Chaotic Resonance in Izhikevich Neuron Model.

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

Dependence of spike timing on signal strength A in periodic state.(a) Mean of inter spike interval < Tk >. (b) Spike timing  against input signal. (a = 0.2, b = 2, c = −56, d = −10, I = −99, f0 = 0.1).
© Copyright Policy
Related In: Results  -  Collection

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

pone.0138919.g009: Dependence of spike timing on signal strength A in periodic state.(a) Mean of inter spike interval < Tk >. (b) Spike timing against input signal. (a = 0.2, b = 2, c = −56, d = −10, I = −99, f0 = 0.1).
Mentions: Fig 8 shows the time series of v(t) (bottom) and the corresponding cycle histogram of the firing counts (top). In case d = −16 ((a)), the neuron fired non-periodically and the cycle histogram responded to the signal with some delay ∣τ∣ ≈ 3[ms]. However, when we changed the value of d to the periodic region, as shown in d = −10 ((b)), the neuron fired periodically and the cycle histogram did not respond to signal . Added to this, we investigated the signal response in the periodic region in detail. Fig 9 indicates < Tk > ((a)) and distribution of ((b)) as a function of A in case d = −10. In 1 × 10−3 ≲ A ≲ 2 × 10−2, < Tk > kept about 8.7 [ms] as a period of autonomous spiking (dashed line) and spread over entire area (−5 to 5 [ms]) uniformly. However, < Tk > began to converge to 10(= T0) [ms] with increasing A in 2 × 10−2 ≲ A ≲ 1. In this region, tended to gather at the specific points by the interaction effect of S(t). Here, the signal amplitude (A = 0.3) used in Fig 8 belonged to this region. In cases of higher signal strength (1 ≲ A ≲ 3), < Tk > and were locked at 10(= T0) [ms] and some specific point within −3.5 ≲ ≲ −1.5 [ms], respectively.

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