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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.


Chaotic system behavior for d = −16.(a) Time evolution of v(t). (b) Its trajectory in the (v, u) phase plane. The dashed line represents the v-cline (v′ = 0) and the dotted line represents the u-cline (u′ = 0). The arrows indicate the vector field of v and u. (c) The return map of (ui, ui + 1), where the solid line represents the orbit of ui, the dotted line represents the solution of ui + 1 = ψ(ui), and the dashed line depicts ui + 1 = ui. (a = 0.2, b = 2, c = −56, I = −99, d = −16).
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pone.0138919.g002: Chaotic system behavior for d = −16.(a) Time evolution of v(t). (b) Its trajectory in the (v, u) phase plane. The dashed line represents the v-cline (v′ = 0) and the dotted line represents the u-cline (u′ = 0). The arrows indicate the vector field of v and u. (c) The return map of (ui, ui + 1), where the solid line represents the orbit of ui, the dotted line represents the solution of ui + 1 = ψ(ui), and the dashed line depicts ui + 1 = ui. (a = 0.2, b = 2, c = −56, I = −99, d = −16).

Mentions: The Izhikevich neuron model can reproduce major firing patterns, such as regular spiking, intrinsically bursting, chattering, and fast spiking [3, 4]. Moreover, research has suggested that this model can simulate chaotic behavior with appropriate parameter values (a = 0.2, b = 2, c = −56, d = −16, I = −99 in Eqs (1) and (2) [4]. Fig 2 (a) and (b) show the chaotic time evolution of v(t) and the strange attractor in a phase plane (v, u), respectively. We also examine the strange attractor in greater detail by using the Poincaré sections Ψ (v = 30 [mV]). The dynamics of (u1, u2,⋯, uN), which is the evolution of u over time on Ψ, is defined as a Poincaré mapping ui + 1 = ψ(ui). As shown in Fig 2(c), on the return map (ui, ui + 1), the solution for ui + 1 = ψ(ui), the orbit of ui and ui + 1 = ui are indicated by dotted, solid, and dashed lines, respectively. It has been observed that the orbit of ui exhibits chaotic behavior in the range −102 ≲ ui ≲ −90, and the shape of ψ displays a stretching and folding structure as a feature of the non-linear map.


Analysis of Chaotic Resonance in Izhikevich Neuron Model.

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

Chaotic system behavior for d = −16.(a) Time evolution of v(t). (b) Its trajectory in the (v, u) phase plane. The dashed line represents the v-cline (v′ = 0) and the dotted line represents the u-cline (u′ = 0). The arrows indicate the vector field of v and u. (c) The return map of (ui, ui + 1), where the solid line represents the orbit of ui, the dotted line represents the solution of ui + 1 = ψ(ui), and the dashed line depicts ui + 1 = ui. (a = 0.2, b = 2, c = −56, I = −99, d = −16).
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4589341&req=5

pone.0138919.g002: Chaotic system behavior for d = −16.(a) Time evolution of v(t). (b) Its trajectory in the (v, u) phase plane. The dashed line represents the v-cline (v′ = 0) and the dotted line represents the u-cline (u′ = 0). The arrows indicate the vector field of v and u. (c) The return map of (ui, ui + 1), where the solid line represents the orbit of ui, the dotted line represents the solution of ui + 1 = ψ(ui), and the dashed line depicts ui + 1 = ui. (a = 0.2, b = 2, c = −56, I = −99, d = −16).
Mentions: The Izhikevich neuron model can reproduce major firing patterns, such as regular spiking, intrinsically bursting, chattering, and fast spiking [3, 4]. Moreover, research has suggested that this model can simulate chaotic behavior with appropriate parameter values (a = 0.2, b = 2, c = −56, d = −16, I = −99 in Eqs (1) and (2) [4]. Fig 2 (a) and (b) show the chaotic time evolution of v(t) and the strange attractor in a phase plane (v, u), respectively. We also examine the strange attractor in greater detail by using the Poincaré sections Ψ (v = 30 [mV]). The dynamics of (u1, u2,⋯, uN), which is the evolution of u over time on Ψ, is defined as a Poincaré mapping ui + 1 = ψ(ui). As shown in Fig 2(c), on the return map (ui, ui + 1), the solution for ui + 1 = ψ(ui), the orbit of ui and ui + 1 = ui are indicated by dotted, solid, and dashed lines, respectively. It has been observed that the orbit of ui exhibits chaotic behavior in the range −102 ≲ ui ≲ −90, and the shape of ψ displays a stretching and folding structure as a feature of the non-linear map.

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.