Sou Nobukawa

Chaotic states induced by resetting process in Izhikevich neuron model

Abstract Several hybrid neuron models, which combine continuous spike-generation mechanisms and discontinuous resetting process after spiking, have been proposed as a simple transition scheme for membrane potential between spike and hyperpolarization. As one of the hybrid spiking neuron models, Izhikevich neuron model can reproduce major spike patterns observed in the cerebral cortex only by tuning a few parameters and also exhibit chaotic states in specific conditions. However, there are a few studies concerning the chaotic states over a large range of parameters due to the difficulty of dealing with the state dependent jump on the resetting process in this model. In this study, we examine the dependence of the system behavior on the resetting parameters by using Lyapunov exponent with saltation matrix and Poincaré section methods, and classify the routes to chaos.

Enhancement of Spike-Timing-Dependent Plasticity in Spiking Neural Systems with Noise

Synaptic plasticity is widely recognized to support adaptable information processing in the brain. Spike-timing-dependent plasticity, one subtype of plasticity, can lead to synchronous spike propagation with temporal spiking coding information. Recently, it was reported that in a noisy environment, like the actual brain, the spike-timing-dependent plasticity may be made efficient by the effect of stochastic resonance. In the stochastic resonance, the presence of noise helps a nonlinear system in amplifying a weak (under barrier) signal. However, previous studies have ignored the full variety of spiking patterns and many relevant factors in neural dynamics. Thus, in order to prove the physiological possibility for the enhancement of spike-timing-dependent plasticity by stochastic resonance, it is necessary to demonstrate that this stochastic resonance arises in realistic cortical neural systems. In this study, we evaluate this stochastic resonance phenomenon in the realistic cortical neural system described by the Izhikevich neuron model and compare the characteristics of typical spiking patterns of regular spiking, intrinsically bursting and chattering experimentally observed in the cortex.

Analysis of Chaotic Resonance in Izhikevich Neuron Model.

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.

Chaotic resonance in Izhikevich neuron model and its assembly

Chaotic Resonance (CR) is known as a phenomenon like Stochastic Resonance (SR) without stochastic noise. SR in which the presence of noise helps a nonlinear system in amplifying a weak (under barrier) signal has been observed in neural systems. However CR has scarcely been examined in the neural systems and recently the concern with the responses in CR in neural systems has been growing. In this paper, we evaluate the signal response in CR in the promising Izhikevich neuron model and its assembly. It is confirmed that chaotic states in CR can respond to the weak signal which is not able to be sensed by periodic stable states.

Chaotic resonance in coupled inferior olive neurons with the llinás approach neuron model

It is well known that cerebellar motor control is fine-tuned by the learning process adjusted according to rich error signals from inferior olive (IO) neurons. Schweighofer and colleagues proposed that these signals can be produced by chaotic irregular firing in the IO neuron assembly; such chaotic resonance (CR) was replicated in their computer demonstration of a Hodgkin-Huxley (HH)-type compartment model. In this study, we examined the response of CR to a periodic signal in the IO neuron assembly comprising the Llinás approach IO neuron model. This system involves empirically observed dynamics of the IO membrane potential and is simpler than the HH-type compartment model. We then clarified its dependence on electrical coupling strength, input signal strength, and frequency. Furthermore, we compared the physiological validity for IO neurons such as low firing rate and sustaining subthreshold oscillation between CR and conventional stochastic resonance (SR) and examined the consistency with asynchronous firings indicated by the previous model-based studies in the cerebellar learning process. In addition, the signal response of CR and SR was investigated in a large neuron assembly. As the result, we confirmed that CR was consistent with the above IO neuron’s characteristics, but it was not as easy for SR.

Analysis of routes to chaos in Izhikevich neuron model with resetting process

Recently, according to the development of the brain measurement technology, it has been recognized that the information is transmitted among neurons by the spike timing instead of the firing rate of neurons. Therefore, the spiking neuron models which can describe the spike timing have been attracting a lot of attention. Izhikevich neuron model, which combines continuous spike-generation mechanisms and discontinuous resetting process after spikes as a hybrid system, can reproduce major spike patterns observed in the cerebral cortex only by tuning a few parameters of it and also exhibit chaotic states in specific conditions. However, there are a few studies concerning the chaotic states over a large range of parameters due to the difficulty of dealing with the state dependent jump on the resetting process in this model. In this study, we examine the dependence of the system behavior on the resetting parameters by using Lyapunov exponent with saltation matrix and Poincaré section methods, and classify the routes to chaos.

Temporal-specific roles of fractality in EEG signal of Alzheimer's disease

A growing number of nonlinear EEG studies have elucidated the reduced fractality in Alzheimers disease (AD). However, despite the importance of studying EEG dynamics within physiologically relevant frequency ranges, far fewer studies have explored temporal-dependent fractal properties in AD. This study was aimed at assessing the temporal-scale specific fractal properties in AD using Higuchis fractal algorithm. As a result, we found both enhanced and reduced fractality in a temporal-scale relevant manner. Our findings suggest that investigating temporal specific fractal properties in EEG might serve as a useful approach for characterizing neural basis of AD.

Analysis of Coherence Resonance in Kaldor-Kalecki Business Cycle Model

It is well known that additive noise brings qualitative transformations of system behavior in a non-linear system as noise-induced phenomena. Recently, Bashkirtseva et al. have shown that this noise-induced phenomenon arises in the Kaldor-Kalecki business cycle model with multiple attractors. However, the economic validity of this condition has not been studied. In this study, we focus on a threshold characteristic of the Kaldor-Kalecki business cycle model under the bias of income and show that coherence resonance can be produced by the effect of this threshold characteristic as one of the noise-induced phenomena.

Chaotic states caused by discontinuous resetting process in spiking neuron model.

Spiking neuron models, which can realize diverse kinds of neural coding by describing spiking activity of membrane potential, have been widely utilized. Among these models, several hybrid spiking neuron models, which combine continuous spike-generation mechanisms and discontinuous resetting process after spiking, have been proposed as a simple transition scheme for membrane potential between spike and hyperpolarization. Izhikevich neuron model as this kind of model can reproduce many spiking patterns. It has also become clear that this model has various kinds of bifurcation and routes to chaos under the effect of the state dependent jump in the resetting process. In response to this situation, we have further gotten interested in the relation between chaotic behaviors and the state dependent jump. In this paper, we approach the subject from the comparison of spiking neuron models without the resetting process and with it. We first adopt a continuous two-dimensional spiking neuron model where the orbit at spiking state does not exhibit the divergent behavior and next insert the resetting process to it.

Evaluation of Chaotic Resonance by Lyapunov Exponent in Attractor-Merging Type Systems

Fluctuating activities in the deterministic chaos cause a phenomenon that is similar to stochastic resonance (SR) whereby the presence of noise helps a non-linear system to amplify a weak (under-barrier) signal. In this phenomenon, called chaotic resonance (CR), the system responds to the weak input signal by the effect of intrinsic chaotic activities under the condition where no additive noise exists. Recently, we have revealed that the signal response of the CR in the spiking neuron model has an unimodal maximum with respect to the degree of stability for chaotic orbits quantified by maximum Lyapunov exponent. In response to this situation, in this study, focusing on CR in the systems with chaos-chaos intermittency, we examine the signal response in a cubic map and a chaotic neural network embedded two symmetric patterns by cross correlation and Lyapunov exponent (or maximum Lyapunov exponent). As the results, it is confirmed that the efficiency of the signal response has a peak at the appropriate instability of chaotic orbit in both systems. That is, the instability of chaotic orbits in CR can play a role the noise strength of SR in not only spiking neural systems but also the systems with chaos-chaos intermittency.