Neural Bursting and Synchronization Emulated by Neural Networks and Circuits

© 2021 IEEE - All rights reserved. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1109/TCSI.2021.3081150Nowadays, research, modeling, simulation and realization of brain-like systems to reproduce brain behaviors have become urgent requirements. In this paper, neural bursting and synchronization are imitated by modeling two neural network models based on the Hopfield neural network (HNN). The first neural network model consists of four neurons, which correspond to realizing neural bursting firings. Theoretical analysis and numerical simulation show that the simple neural network can generate abundant bursting dynamics including multiple periodic bursting firings with different spikes per burst, multiple coexisting bursting firings, as well as multiple chaotic bursting firings with different amplitudes. The second neural network model simulates neural synchronization using a coupling neural network composed of two above small neural networks. The synchronization dynamics of the coupling neural network is theoretically proved based on the Lyapunov stability theory. Extensive simulation results show that the coupling neural network can produce different types of synchronous behaviors dependent on synaptic coupling strength, such as anti-phase bursting synchronization, anti-phase spiking synchronization, and complete bursting synchronization. Finally, two neural network circuits are designed and implemented to show the effectiveness and potential of the constructed neural networks.Peer reviewe

Dynamic Behavior Analysis and Synchronization of Memristor-Coupled Heterogeneous Discrete Neural Networks

© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).Continuous memristors have been widely studied in recent years; however, there are few studies on discrete memristors in the field of neural networks. In this paper, a four-stable locally active discrete memristor (LADM) is proposed as a synapse, which is used to connect a two-dimensional Chialvo neuron and a three-dimensional KTZ neuron, and construct a simple heterogeneous discrete neural network (HDNN). Through a bifurcation diagram and Lyapunov exponents diagram, the period and chaotic regions of the discrete neural network model are shown. Through numerical analysis, it was found that the chaotic region and periodic region of the neural network based on DLAM are significantly improved. In addition, coexisting chaos and chaos attractors, coexisting periodic and chaotic attractors, and coexisting periodic and periodic attractors will appear when the initial value of the LADM is changed. Coupled by a LADM synapse, two heterogeneous discrete neurons are gradually synchronized by changing the coupling strength. This paper lays a good foundation for the future analysis of LADMs and the related research of discrete neural networks coupled by LADMs.Peer reviewe

Dynamics Days Latin America and the Caribbean 2018

This book contains various works presented at the Dynamics Days Latin America and the Caribbean (DDays LAC) 2018. Since its beginnings, a key goal of the DDays LAC has been to promote cross-fertilization of ideas from different areas within nonlinear dynamics. On this occasion, the contributions range from experimental to theoretical research, including (but not limited to) chaos, control theory, synchronization, statistical physics, stochastic processes, complex systems and networks, nonlinear time-series analysis, computational methods, fluid dynamics, nonlinear waves, pattern formation, population dynamics, ecological modeling, neural dynamics, and systems biology. The interested reader will find this book to be a useful reference in identifying ground-breaking problems in Physics, Mathematics, Engineering, and Interdisciplinary Sciences, with innovative models and methods that provide insightful solutions. This book is a must-read for anyone looking for new developments of Applied Mathematics and Physics in connection with complex systems, synchronization, neural dynamics, fluid dynamics, ecological networks, and epidemics

Unified approach to catastrophic events: from the normal state to geological or biological shock in terms of spectral fractal and nonlinear analysis

An important question in geophysics is whether earthquakes (EQs) can be anticipated prior to their occurrence. Pre-seismic electromagnetic (EM) emissions provide a promising window through which the dynamics of EQ preparation can be investigated. However, the existence of precursory features in pre-seismic EM emissions is still debatable: in principle, it is difficult to prove associations between events separated in time, such as EQs and their EM precursors. The scope of this paper is the investigation of the pre-seismic EM activity in terms of complexity. A basic reason for our interest in complexity is the striking similarity in behavior close to irreversible phase transitions among systems that are otherwise quite different in nature. Interestingly, theoretical studies (Hopfield, 1994; Herz and Hopfield 1995; Rundle et al., 1995; Corral et al., 1997) suggest that the EQ dynamics at the final stage and neural seizure dynamics should have many similar features and can be analyzed within similar mathematical frameworks. Motivated by this hypothesis, we evaluate the capability of linear and non-linear techniques to extract common features from brain electrical activities and pre-seismic EM emissions predictive of epileptic seizures and EQs respectively. The results suggest that a unified theory may exist for the ways in which firing neurons and opening cracks organize themselves to produce a large crisis, while the preparation of an epileptic shock or a large EQ can be studied in terms of ''Intermittent Criticality''

Comparative study between radiofrequency-induced and muscimol-induced inhibition of cultured networks of cortical neuron

Previous studies have shown that spontaneously active cultured networks of cortical neuron grown planar microelectrode arrays are sensitive to radiofrequency (RF) fields and exhibit an inhibitory response more pronounced as the exposure time and power increase. To better understand the mechanism behind the observed effects, we aimed at identifying similarities and differences between the inhibitory effect of RF fields (continuous wave, 1800 MHz) to the γ-aminobutyric acid type A (GABAA) receptor agonist muscimol (MU). Inhibition of the network bursting activity in response to RF exposure became apparent at an SAR level of 28.6 W/kg and co-occurred with an elevation of the culture medium temperature of ~1°C. Exposure to RF fields preferentially inhibits bursting over spiking activity and exerts fewer constraints on neural network bursting synchrony, differentiating it from a pharmacological inhibition with MU. Network rebound excitation, a phenomenon relying on the intrinsic properties of cortical neurons, was observed following the removal of tonic hyperpolarization after washout of MU but not in response to cessation of RF exposure. This implies that hyperpolarization is not the main driving force mediating the inhibitory effects of RF fields. At the level of single neurons, network inhibition induced by MU and RF fields occurred with reduced action potential (AP) half-width. As changes in AP waveform strongly influence efficacy of synaptic transmission, the narrowing effect on AP seen under RF exposure might contribute to reducing network bursting activity. By pointing only to a partial overlap between the inhibitory hallmarks of these two forms of inhibition, our data suggest that the inhibitory mechanisms of the action of RF fields differ from the ones mediated by the activation of GABAA receptors