Complex Synchronization of a Ring-Structured Network of FitzHugh-Nagumo Neurons With Single-and Dual-State Gap Junctions Under Ionic Gates and External Electrical Disturbance

Abstract

Synchronization plays an essential role in processing information and decisions by neurons and their networks in the brain, and it is useful to study the synchronization of neuron networks, as a part of the process of understanding the functionality of both healthy and diseased brains. In the past, most studies had developed control schemes relating to synchronization problems which were limited to two or three neurons, which cannot depict the dynamic synchronization behavior of neuron networks. In this paper, we investigated the synchronization issues associated with a ring-structured network of FitzHugh-Nagumo (FHN) neurons, under external electrical stimulation, and with single-and dual-state gap junctions. In addition, the gap junctions (coupling)s and ionic gate disturbances were included in the dynamics of this FHN neuronal network, making our work both more realistic, and more challenging. Thus, each neuron in this network was influenced synaptically by its neighboring two neurons. A simple, robust, and adaptive control scheme, for both a single-and the dual-gap-junction network has been proposed, which will compensate for the nonlinear dynamics without direct cancelation to achieve synchronization. Sufficient conditions to guarantee synchronization of both membrane potentials and recovery variables were derived by using Lyapunov stability theory. Finally, the proposed scheme was validated, and its efficacy was comprehensively analyzed through numerical simulations.

Lag synchronization of coupled time-delayed FitzHugh–Nagumo neural networks via feedback control

“…Among those, FHN is the most commonly used model to investigate the synchronization of coupled neurons because of its wide applicability and complex dynamical aspects. In the literature, the subject of neuronal synchronization, using the FHN model, has been intensively examined as a potential application in cognitive engineering 1,20,28,47,57 . Researchers have developed adaptive 20,41 , nonlinear 28 , robust control 23 , neuralnetwork-, fuzzy 74 , and observer-based control schemes 63 to study the synchronization phenomenon in FHN www.nature.com/scientificreports/ neurons under external electrical stimulations.…”

“…Let us consider a bidirectional ring-structured time-delayed FHN network with different gap junctions and external noise. Mathematically, (1) www.nature.com/scientificreports/ where ϕ 2 (t) is the Gaussian noise 70 source having zero mean and the following correlation function:…”

“…Synchronization plays a tremendous role in information transfer and decision-making in different fields of science and technology 1 . In the past decade, many researchers have investigated different synchronization schemes, methodologies, and regimes for chaotic systems such as lag synchronization 2 , generalized synchronization 3 , phase synchronization 4 , projective synchronization 5 , anticipating synchronization 6 , cluster synchronization 7 , and consecutive synchronization 8 .…”

“…Wang et al studied the synchronization phenomenon in the time-delayed chaotic system with unknown and uncertain parameters and developed an intermittent adaptive control scheme to guarantee synchronization between neurons 41 . Ibrahim and Jung developed an adaptive control methodology to guarantee synchronization between a bidirectional ring-structured FHN neuronal network under the effect of external electrical stimulation with single- and dual-state gap junctions 1 . Zhang investigated the out-lag synchronization by proposing a pinning control scheme in fractional-order complex networks with coupling and internal delays 59 .…”

Adaptive Deep Learning for Time-Varying Systems With Hidden Parameters: Predicting Changing Input Beam Distributions of Compact Particle Accelerators

“…Our approach of combining external feedbacks with neural networks is analogous to a natural phenomenon in biological systems in which networks of neurons interact with each other and are controlled by external feedback loops and other networks 29 . For example recent studies have shown that the challenging task of synchronization between neuron networks can be achieved by feedback controls in the presence of signal delay, noise, and external disturbances 30,31 , and that resonance can be excited and controlled in complex neuron systems by using external feedback signals including chaotic resonances 32,33 . Some initial simplified adaptive ML studies have also begun on coupling the outputs of CNNs to adaptive feedback for real-time accelerator phase space control 34 and for predicting 3D electron density distributions for 3D coherent diffraction imaging 35 .…”