Design of an analog chaos-generating circuit using piecewise-constant dynamics

Tsubone, Tadashi; Saito, Toshimichi; Inaba, Nobuyuki

doi:10.1093/ptep/ptw037

Cited by 9 publications

(6 citation statements)

References 19 publications

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“…The hybrid spiking neuron model is one of the piecewise-smooth dynamical systems, in which dynamics are switched according to the state of the system 38 . Saito and colleagues have conducted chaos/bifurcation analysis and circuit implementation against piecewise-constant dynamical systems, and piecewise-linear dynamical systems, as simplified versions of the piecewise-smooth dynamical system 39 – 41 . In particular, Tsubone et al .…”

Section: Introductionmentioning

confidence: 99%

“…In particular, Tsubone et al . proposed a systematic method to predict parameter regions for chaotic states using an analytical approach in the piecewise-constant dynamical system 41 . While in general, piecewise-smooth dynamical systems include non-linear terms similar to those seen in the Izhikevich neuron model, an approach for evaluating Lyapunov exponents and characteristic multipliers that considers the saltation matrix 38 through simulations against exhaustive parameter sets is needed.…”

Section: Introductionmentioning

confidence: 99%

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Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model

Nobukawa

Nishimura

Yamanishi

2017

Sci Rep

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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.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model

Nobukawa

Nishimura

Yamanishi

2017

Sci Rep

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“…The transient processes occur in these circuits under constant excitation, for example the charge or discharge of the capacitor at constant current. The analysis of AN behavior of such type and networks based on them is given in papers [47][48]. The nonlinearity of the memristor characteristics due to the change in its resistance when current flows through device limits the development of PWC memristor based oscillators [49,50].…”

Section: Introductionmentioning

confidence: 99%

Functional Capabilities of Coupled Memristor-Based Reactance-Less Oscillators

Rakitin¹,

Русаков²

2021

Memristor - An Emerging Device for Post-Moore’s Computing and Applications

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New functionalities of reactance-less memristor based oscillators are discussed which arise when two elementary oscillators are connected. It is shown that the system of coupled memristor based oscillators can be used for converting analog and analog-digital signals into binary pulse sequences. The approach to control the thresholds in memristor based oscillators is discussed. Standard control approach in memristor based oscillators is the exploitation of input signal to drive the rate of change in the state of the memristor. In contrast, the main idea of the considered controlling approach is to send the input signal not directly to the memristor device but to the comparator circuit and as result to control oscillator circuit behavior by change of interval of memristor resistor variation. The capabilities of coupled memristor based oscillators with control thresholds are sufficient for constructing the simple circuit elements of oscillatory computing architectures.

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“…Saito et al . conducted chaos and bifurcation analysis and circuit implementation using the piecewise-constant and piecewise-linear systems as types of piecewise-smooth systems 19 – 23 . Tsubone et al .…”

Section: Introductionmentioning

confidence: 99%

“…Tsubone et al . 23 proposed a systematic method using an analytical approach to predict the parameter regions for the chaotic states in piecewise-constant systems. Meanwhile, Mitsubori and Saito 19 and Nakano and Saito 20 developed a systematic method for piecewise-linear systems.…”

Section: Introductionmentioning

confidence: 99%

Routes to Chaos Induced by a Discontinuous Resetting Process in a Hybrid Spiking Neuron Model

Nobukawa

Nishimura

Yamanishi

2018

Sci Rep

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Several hybrid spiking neuron models combining continuous spike generation mechanisms and discontinuous resetting processes following spiking have been proposed. The Izhikevich neuron model, for example, can reproduce many spiking patterns. This model clearly possesses various types of bifurcations and routes to chaos under the effect of a state-dependent jump in the resetting process. In this study, we focus further on the relation between chaotic behaviour and the state-dependent jump, approaching the subject by comparing spiking neuron model versions with and without the resetting process. We first adopt a continuous two-dimensional spiking neuron model in which the orbit in the spiking state does not exhibit divergent behaviour. We then insert the resetting process into the model. An evaluation using the Lyapunov exponent with a saltation matrix and a characteristic multiplier of the Poincar’e map reveals that two types of chaotic behaviour (i.e. bursting chaotic spikes and near-period-two chaotic spikes) are induced by the resetting process. In addition, we confirm that this chaotic bursting state is generated from the periodic spiking state because of the slow- and fast-scale dynamics that arise when jumping to the hyperpolarization and depolarization regions, respectively.

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Design of an analog chaos-generating circuit using piecewise-constant dynamics

Cited by 9 publications

References 19 publications

Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model

Chaotic Resonance in Typical Routes to Chaos in the Izhikevich Neuron Model

Functional Capabilities of Coupled Memristor-Based Reactance-Less Oscillators

Routes to Chaos Induced by a Discontinuous Resetting Process in a Hybrid Spiking Neuron Model

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