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Article
Physics, Multidisciplinary
Dong Yu et al.
Summary: This paper investigates the influence of topology on the phenomenon of delay-induced multiple resonances in locally driven systems. The results show that the maximum value of the Fourier coefficient occurs at an integer multiple of T/N, where T is the external signal period or the neuronal intrinsic oscillation period, and N is determined by the network's topology. The obtained results are briefly discussed in terms of the network's topology. The emergence of delay-induced multiple resonances depends on the interaction of the delay enhancement effect and the delay inhibition effect. In the case of weak coupling, the signal response performance is enhanced over a wider range of delay windows, dominated by delay enhancement effects. These findings may provide new insights into weak signal response and transmission in delay-coupled neural networks.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2023)
Article
Mathematics
Minglin Ma et al.
Article
Engineering, Electrical & Electronic
Shan Wang et al.
Summary: This paper investigates the synchronization of memristive Hindmarsh-Rose neuron maps under different coupling conditions, including electrical synapses, chemical synapses, inner linking functions, and hybrid synapses. The study found that synchronization is achieved when the neurons are coupled through electrical and hybrid synapses, but not through chemical synapses. Moreover, it shows that a slightly lower coupling value is needed for synchronization through inner linking functions compared to electrical synapses.
AEU-INTERNATIONAL JOURNAL OF ELECTRONICS AND COMMUNICATIONS
(2023)
Article
Mathematics, Interdisciplinary Applications
Qianming Ding et al.
Summary: In this paper, a two-compartment model is proposed to study the effects of morphology and temperature on neuronal kinetics. The metabolic energy consumption of neurons with different morphologies and temperatures is calculated using the equivalent circuit method. It is found that higher temperatures increase energy efficiency, while moderate morphologies result in higher firing rates but also higher energy costs. The integration of this model into a feedforward network shows that moderate temperature and morphology allow stable propagation of synchronization spikes and maximize energy utilization for information transmission. A simple statistical method is also introduced to evaluate the robustness of network information transmission. This paper provides insights for further studies on energy consumption in the cerebral cortex.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Condensed Matter
Feifei Yang et al.
Summary: A simple neural circuit coupled by magnetic flux-controlled memristor is used to describe the electromagnetic effect and radiation on biological neurons. The effect of external electric field on biophysical neurons is identified by adding a charge-controlled memristor into a nonlinear circuit. The firing patterns of the memristive circuit can be adjusted by tuning the angular frequency of an external voltage source, and the physical field energy and equivalent Hamilton energy are dependent on the firing modes of neural activities. The exchange and propagation of field energy in clustered neurons is achieved by regulating the charge flow, and coupling intensity is controlled by the energy difference between adjacent neurons for perfect energy balance and saturation.
EUROPEAN PHYSICAL JOURNAL B
(2023)
Article
Computer Science, Artificial Intelligence
Zhihao Zuo et al.
Summary: This article introduces a method to achieve system synchronization at different scales using recurrent neural networks, and proposes a definition of synchronization at a macroscopic level, called hyper-synchronization. The effectiveness of this method is demonstrated through numerical experiments, and guidance is provided for synchronization among multiple reservoir computers with different structures. This work provides an appealing framework for achieving synchronization of neural networks, with potential applications in areas such as communications and biological systems.
Article
Mathematics, Applied
Sridevi Sriram et al.
Summary: The network connectivities are crucial for exhibiting diverse collective dynamics in complex systems. Hindmarsh-Rose neurons connected by electromagnetic interactions are used to demonstrate different dynamical states and transitions. Specifically, the dynamical behaviors of the system are explored under regular, small-world, and random network connectivities. The results show that increasing coupling intensity leads to a transition from desynchronization to traveling wave state for all considered network interactions. Furthermore, the investigation is extended to a three-layer multiplex network where synchronization is achieved in all layers with increasing coupling intensity, eventually reaching a rest state at high coupling strength.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Interdisciplinary Applications
Tianyu Li et al.
Summary: This paper investigates how neuronal morphology and network properties modulate signal propagation in a multi-layer feedforward network (FFN) using a biophysical two-compartment model. The results show that neurons with larger dendrites and the output layer of FFN constructed by larger-dendrite neurons exhibit better responses to weak signals. Sparse connection and weak synaptic strength optimize the responses of the output layer, and a suitable chaotic current is necessary for successful propagation.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Interdisciplinary Applications
Quan Xu et al.
Summary: This study proposes a memristive Hodgkin-Huxley circuit based on second-order and first-order local active memristors (LAMs) to simulate the complex nonlinearities of sodium and potassium ion channels, thus generating abundant spiking firing patterns. Numerical simulations and hardware experiments demonstrate the effectiveness of the circuit in generating periodic and chaotic spiking firing patterns.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Physics, Applied
Mohd Taib Shatnawi et al.
Article
Mathematics, Interdisciplinary Applications
Minglin Ma et al.
Summary: To enrich the dynamic behaviors of discrete neuron models and mimic biological neural networks more effectively, this paper proposes a bistable locally active discrete memristor (LADM) model to simulate synapses. By introducing the LADM into two identical Rulkov neurons, the dynamic behaviors of neural networks are explored. Numerical simulation shows that the neural network exhibits multistability and new firing behaviors under different system parameters and initial values. In addition, the synchronization between the neurons is also investigated.
FRACTAL AND FRACTIONAL
(2023)
Article
Physics, Multidisciplinary
Yan-Mei Lu et al.
Summary: This study constructed a new fractional-order discrete memristor model with significant nonlinearity for simulating the dynamical behaviors of neurons under electromagnetic radiation. The characteristics of integer-order and fractional-order systems were analyzed, showing that the fractional-order system has richer dynamics.
Review
Engineering, Mechanical
Minglin Ma et al.
Summary: This paper introduces a locally active discrete memristor model for the first time and analyzes its dynamical behaviors using various methods. The results show that applying the locally active discrete memristor significantly improves the chaotic properties of the map and demonstrates the existence of attractors.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Mechanical
Chunlai Li et al.
Summary: This paper introduces a nonvolatile locally active memristor with three stable equilibrium states for three-bit-per-cell memory device functionality. A neural network model composed of three Hopfield neurons is presented, showing that the distribution of system equilibrium points depends on the coupling weight of the memristor synapse. The bifurcation diagram reveals the coexistence phenomenon of multiple stable modes, with complex bursting oscillation emerging in the neural network when there is a step difference between the system's natural frequency and the external excitation frequency.
NONLINEAR DYNAMICS
(2022)
Article
Engineering, Electrical & Electronic
Yan Liang et al.
Summary: Locally-active memristor (LAM) has potential applications in neuromorphic computing as an artificial neuron. Quantitative theoretical analysis on LAMs shows that their performance is closely associated with three crucial parameters: resistance, differential resistance, and a dynamic parameter. These parameters can be used to derive the small-signal equivalent circuit of LAMs and determine the oscillation frequency range and conditions for LAM-based oscillators.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2022)
Article
Physics, Multidisciplinary
Xu Ma et al.
Summary: In this study, the complex neuromorphological dynamics observed when a locally active memristor is applied to the Hindmarsh-Rose neuron are discussed. The results show that the rotation control can effectively influence the amplitude of neuron bursting without causing dynamics switching. The design of the rotation control matrix is found to be crucial for amplitude control.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Applied
M. Paul Asir et al.
Summary: We present a model that simulates the dynamics of oscillators coupled by mean-field nonlinear memductance. The dynamic nonlinearity generated by nonlinear memductance causes the coupling direction to change over time. Depending on the parameters, this dynamic coupling leads the oscillators to synchronization or anti-synchronization. Specifically, we observe anti-phase and intermittent synchronization depending on the forcing frequency and coupling strength. By increasing the coupling magnitude, we observe a transition from intermittent synchronization to complete synchronization through anti-phase synchronization. Numerical simulations validate the results. This hypothesis has significant implications for the study of neuronal networks.
Article
Physics, Multidisciplinary
Sathiyadevi Kanagaraj et al.
Summary: In this paper, the dynamical behavior of a flux coupled conductance-based neuron under external periodic stimulus is investigated. The transitions between periodic and chaotic attractors, as well as the antimonotonicity phenomenon, are examined through bifurcation analysis and Lyapunov exponents. The collective dynamical behaviors of the neuron network under the influence of propagation noise are also explored, revealing transitions from desynchronized to synchronized states in the presence of noise, and the potential aid of noise in synchronization even at weak coupling strength.
EUROPEAN PHYSICAL JOURNAL PLUS
(2022)
Article
Mathematics, Interdisciplinary Applications
Premraj Durairaj et al.
Summary: This study examines the existence of strange nonchaotic attractors (SNAs) using a memristor-based Shimizu-Morioka oscillator. The birth and mechanism of SNAs are analyzed through rational approximation theory and validated through various nonlinear dynamical characterizations. Experimental evidence is also provided to inspect the occurrence of SNAs.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2022)
Article
Mathematics, Interdisciplinary Applications
Kexin Li et al.
Summary: In this study, a discrete bi-neuron model is used to examine the effects of memory resistance on neuronal coupling, synchronization behavior, and dynamical behavior. The results demonstrate the coexistence of multiple firing patterns and provide evidence for the realization of synchronous control of coupled neurons.
CHAOS SOLITONS & FRACTALS
(2022)
Article
Engineering, Mechanical
Zhijun Li et al.
Summary: Local activity is considered as the origin of complexity, with locally active memristor proposed in this study exhibiting multiple firing patterns under different initial conditions. The study also investigates phase synchronization of synapse-coupled neurons. Circuit simulations are included to confirm the effectiveness of numerical simulations.
NONLINEAR DYNAMICS
(2021)
Article
Engineering, Electrical & Electronic
Zhijun Li et al.
Summary: This study introduces a novel locally active memristor with four-stable pinched hysteresis loops, demonstrating non-volatile memory and local activity. By utilizing this memristor, a memristive Hindmarsh-Rose neuron model is constructed to explore multiple firing patterns, showing that firing rhythms can be regulated by adjusting memristor initial values in different stable regions. Circuit simulations further confirm the theoretical analysis.
ELECTRONICS LETTERS
(2021)
Article
Engineering, Mechanical
Ronghao Li et al.
Summary: This paper proposes a new type of non-volatile locally active memristor with bi-stability, and explains the local activity phenomenon based on mathematical analyses and numerical simulations. A locally active memristive coupled neuron model is constructed to reveal the parameter-associated dynamical behaviors.
NONLINEAR DYNAMICS
(2021)
Article
Mathematics, Applied
Yumei Tan et al.
Article
Engineering, Mechanical
Hairong Lin et al.
NONLINEAR DYNAMICS
(2020)
Article
Physics, Multidisciplinary
Chunlai Li et al.
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
(2019)
Review
Physics, Multidisciplinary
Jun Ma et al.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2019)
Article
Computer Science, Artificial Intelligence
Xudong Xie et al.
Article
Engineering, Electrical & Electronic
Alon Ascoli et al.
IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS I-REGULAR PAPERS
(2015)
Article
Engineering, Electrical & Electronic
Leon Chua
SEMICONDUCTOR SCIENCE AND TECHNOLOGY
(2014)
Article
Nanoscience & Nanotechnology
Leon Chua
Article
Mathematics, Interdisciplinary Applications
Andrew L. Fitch et al.
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
(2012)
Article
Physics, Multidisciplinary
Shiping Wen et al.
Article
Engineering, Electrical & Electronic
Bharathwaj Muthuswamy et al.
IETE TECHNICAL REVIEW
(2009)
