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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.


Time series of membrane potential v(t) (left) and attractor (right).(a) d = −11, (b) d = −12, (c) d = −13, (d) d = −16 (a = 0.2, b = 2, c = −56, I = −99).
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pone.0138919.g005: Time series of membrane potential v(t) (left) and attractor (right).(a) d = −11, (b) d = −12, (c) d = −13, (d) d = −16 (a = 0.2, b = 2, c = −56, I = −99).

Mentions: Furthermore, in the region d ≈ −11.9 as a bifurcation point, the trajectory (v, u) and the time series of v(t) were examined. At d = −11 in Fig 5(a), the time series of v(t) (left) and the trajectory (right) indicate periodic spiking and a one-period state, respectively. As the value of d decreases, the behavior of the system becomes irregular, as shown in Fig 5(b), (c), and (d). It can be observed that the durations of the apparently periodic instances of spiking seemed to have decreased during episodes of chaotic behavior in the system with a reduction in the value of d.


Analysis of Chaotic Resonance in Izhikevich Neuron Model.

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

Time series of membrane potential v(t) (left) and attractor (right).(a) d = −11, (b) d = −12, (c) d = −13, (d) d = −16 (a = 0.2, b = 2, c = −56, I = −99).
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4589341&req=5

pone.0138919.g005: Time series of membrane potential v(t) (left) and attractor (right).(a) d = −11, (b) d = −12, (c) d = −13, (d) d = −16 (a = 0.2, b = 2, c = −56, I = −99).
Mentions: Furthermore, in the region d ≈ −11.9 as a bifurcation point, the trajectory (v, u) and the time series of v(t) were examined. At d = −11 in Fig 5(a), the time series of v(t) (left) and the trajectory (right) indicate periodic spiking and a one-period state, respectively. As the value of d decreases, the behavior of the system becomes irregular, as shown in Fig 5(b), (c), and (d). It can be observed that the durations of the apparently periodic instances of spiking seemed to have decreased during episodes of chaotic behavior in the system with a reduction in the value of d.

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.