Effect of the electromagnetic induction on a modified memristive neural map model

The significance of discrete neural models lies in their mathematical simplicity and computational ease. This research focuses on enhancing a neural map model by incorporating a hyperbolic tangent-based memristor. The study extensively explores the impact of magnetic induction strength on the model's dynamics, analyzing bifurcation diagrams and the presence of multistability. Moreover, the investigation extends to the collective behavior of coupled memristive neural maps with electrical, chemical, and magnetic connections. The synchronization of these coupled memristive maps is examined, revealing that chemical coupling exhibits a broader synchronization area. Additionally, diverse chimera states and cluster synchronized states are identified and discussed

Effects of memristor-based coupling in the ensemble of FitzHugh-Nagumo elements

In this paper, we study the impact of electrical and memristor-based couplings on some neuron-like spiking regimes, previously observed in the ensemble of two identical FitzHugh-Nagumo elements with chemical excitatory coupling. We demonstrate how increasing strength of these couplings affects on such stable periodic regimes as spiking in-phase, anti-phase and sequential activity. We show that the presence of electrical and memristor-based coupling does not essentially affect regimes of in-phase activity. Such regimes do not changes remaining stable ones. However, it is not the case for regimes of anti-phase and sequential activity. All such regimes can transform into periodic or chaotic ones which are very similar to the regimes of in-phase activity. Concerning the regimes of sequential activity, this transformation depends continuously on the coupling parameters, whereas some anti-phase regimes can disappear via a saddle-node bifurcation and nearby orbits tend to regimes of in-phase activity. Also, we show that new interesting neuron-like phenomena can appear from the regimes of sequential activity when increasing the strength of electrical and/or memristor-based coupling. The corresponding regimes can be associated with the appearance of spiral attractors containing a saddle-focus equilibrium with homoclinic orbit and, thus, they correspond to chaotic motions near the invariant manifold of synchronization, which contains all in-phase limit cycles. Such new regimes can lead to the emergence of extreme events in the system of coupled neurons. In particular, the interspike intervals can become arbitrarily large when orbit pass very close to the saddle-focus. Finally, we show that the further increase in the strength of electrical coupling and/or memristor-based coupling leads to decreasing interspike intervals and, thus, it helps to avoid such extreme behavior

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

Chimera states in a multi-weighted neuronal network

There are multiple types of interactions among neurons, each of which has a remarkable effect on the neurons' behavior. Due to the significance of chimeras in neural processes, in this paper, we study the impact of different electrical, chemical, and ephaptic couplings on the emergence of chimera. Consequently, a multi-weighted small-world network of neurons is considered. The simultaneous effects of two and three couplings are explored on the chimera and complete synchronization. The results represent that the synchronization is achieved in very small coupling strengths in the absence of chemical synapses. In contrast, without electrical synapses, the neurons only exhibit chimera behavior. In the three-weighted network, the synchronization is enhanced for special chemical coupling strengths. The network with directed links is also examined. The general behaviors of the directed and undirected networks are the same; however, the directed links lead to lower synchronization error

Firing multistability in a locally active memristive neuron model

Funding Information: This work is supported by The Major Research Project of the National Natural Science Foundation of China (91964108), The National Natural Science Foundation of China (61971185), The Open Fund Project of Key Laboratory in Hunan Universities (18K010). Publisher Copyright: © 2020, Springer Nature B.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.The theoretical, numerical and experimental demonstrations of firing dynamics in isolated neuron are of great significance for the understanding of neural function in human brain. In this paper, a new type of locally active and non-volatile memristor with three stable pinched hysteresis loops is presented. Then, a novel locally active memristive neuron model is established by using the locally active memristor as a connecting autapse, and both firing patterns and multistability in this neuronal system are investigated. We have confirmed that, on the one hand, the constructed neuron can generate multiple firing patterns like periodic bursting, periodic spiking, chaotic bursting, chaotic spiking, stochastic bursting, transient chaotic bursting and transient stochastic bursting. On the other hand, the phenomenon of firing multistability with coexisting four kinds of firing patterns can be observed via changing its initial states. It is worth noting that the proposed neuron exhibits such firing multistability previously unobserved in single neuron model. Finally, an electric neuron is designed and implemented, which is extremely useful for the practical scientific and engineering applications. The results captured from neuron hardware experiments match well with the theoretical and numerical simulation results.Peer reviewedFinal Accepted Versio

Emulation of Neural Dynamics in Neuromorphic Circuits Based on Memristive Devices

The most impressive properties of the human brain are widely acknowledged as being perception and consciousness. While the underlying mechanisms are not yet understood, it is very likely that neural dynamics, in connection with the topology of neural networks, may play a decisive role. Neuromorphic systems offer an interesting approach to emulate and model these processes, as they allow the complexity of neural networks to be mapped onto energy-efficient and real-time capable systems. For this purpose, analogue electrical circuits that are oriented as closely as possible to biological networks are investigated. Electronic devices are particularly important for this purpose, as they make it possible to emulate the mechanisms that are important to the learning and memory processes that occur at the connections of neurons in form of synapses. In this context, it has been shown that nano-ionic mechanisms, in socalled memristive devices, allow the emulation of synaptic plasticity on a descriptive level within a single device. Memristive devices are passive, non-volatile components whose resistance value depends on the applied electrical potentials. In recent years, the important plasticity mechanisms of synaptic information-processing have been emulated using memristive devices. The importance of memristive devices in terms of emulating dynamic processes within novel bio-inspired computing schemes attract worldwide interest and is the subject of this thesis