Neural Bursting and Synchronization Emulated by Neural Networks and Circuits

Abstract

Nowadays, 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.

Memristive electromagnetic induction effects on Hopfield neural network

“…Electronic neuron circuit is nowadays regarded as an excellent artificial block to implement the VLSI applying in neuromorphic computing [38]. It can be achieved in three ways, namely, analog, digital, and hybrid analog/digital circuits [39][40][41][42]. In this section, the memristive HNN model is implemented in analog circuit and the PCB-based hardware experiments are carried out to validate the memristive electromagnetic induction effects.…”

Dynamic analysis and application in medical digital image watermarking of a new multi-scroll neural network with quartic nonlinear memristor

“…Based on HNN, Ref. [ 46 ] simulated neural burst by modeling two kinds of neural network models, and the simple neural network model proposed can produce rich bursting dynamics.…”

Firing mechanism based on single memristive neuron and double memristive coupled neurons

“…Memristor, as the fourth kind of circuit element after resistor, capacitor and inductor, has inherent nonlinearity and plasticity [3,4]. It is often organically combined with other circuit elements to construct application circuits, such as memristive chaotic circuits [5][6][7], memristive neuromorphic circuits [8][9][10] and so on [11]. In particular, memristive neuromorphic circuits can mimic the functions of biological neurons and neural networks, which can exhibit rich and complex firing mechanisms, like spike [12], burst [13][14][15], cycle [16] and chaos [17][18][19][20].…”