Teruya Yamanishi

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.

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.

Approaches of Phase Lag Index to EEG Signals in Alzheimer’s Disease from Complex Network Analysis

The brain is organized as neuronal assemblies with hierarchies of complex network connectivity, and its function is consider to be arisen by synchronized rhythmical firing of neurons. Recently, it is suggested that some of the mental disorders are related to the alterations in the network connectivity in the brain and/or of the strength on synchronized rhythm for brain waves. Here we attempt to analyze electroencephalograms of Alzheimer’s disease by Phase Lag Index (PLI) as an index of the synchronization on signals. By regarding values of PLI as the network connectivity among electrodes, we construct a network for PLI in the brain. So, a clustering coefficient describing structural characteristics of the network are also discussed.

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 Typical Routes to Chaos in the Izhikevich Neuron Model

Chaotic resonance (CR), in which a system responds to a weak signal through the effects of chaotic activities, is a known function of chaos in neural systems. The current belief suggests that chaotic states are induced by different routes to chaos in spiking neural systems. However, few studies have compared the efficiency of signal responses in CR across the different chaotic states in spiking neural systems. We focused herein on the Izhikevich neuron model, comparing the characteristics of CR in the chaotic states arising through the period-doubling or tangent bifurcation routes. We found that the signal response in CR had a unimodal maximum with respect to the stability of chaotic orbits in the tested chaotic states. Furthermore, the efficiency of signal responses at the edge of chaos became especially high as a result of synchronization between the input signal and the periodic component in chaotic spiking activity.

Band-specific atypical functional connectivity pattern in childhood autism spectrum disorder

OBJECTIVE Altered brain connectivity has been theorized as a key neural underpinning of autism spectrum disorder (ASD), but recent investigations have revealed conflicting patterns of connectivity, particularly hyper-connectivity and hypo-connectivity across age groups. The application of graph theory to neuroimaging data has become an effective approach for characterizing topographical patterns of large-scale functional networks. We used a graph approach to investigate alteration of functional networks in childhood ASD. METHOD Magnetoencephalographic signals were quantified using graph-theoretic metrics with a phase lag index (PLI) for specific bands in 24 children with autism spectrum disorder and 24 typically developing controls. RESULTS No significant group difference of PLI was found. Regarding topological organization, enhanced and reduced small-worldness, representing the efficiency of information processing, were observed respectively in ASD children, particularly in the gamma band and delta band. CONCLUSIONS Analyses revealed frequency-dependent atypical neural network topologies in ASD children. SIGNIFICANCE Our findings underscore the recently proposed atypical neural network theory of ASD during childhood. Graph theory with PLI applied to magnetoencephalographic signals might be a useful approach for characterizing the frequency-specific neurophysiological bases of ASD.

Programming instruction using a micro robot as a teaching tool

This practical report analyzes a programming class using a micro robot (MR), the smallest soccer robot in the RoboCup world competition. This class examined the effect of using the MR as the actual equipment employed in programming. Questionnaire results on this class revealed that these teaching materials evoked a heightened programming interest among students. Moreover, the problems related to programming instruction using an MR were better understood; therefore, a strategy for improving the related problems is discussed here.

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.