Lag synchronization of multiple identical Hindmarsh–Rose neuron models coupled in a ring structure

Abstract

Lag synchronization of multiple identical Hindmarsh-Rose neuron systems coupled in a ring structure is investigated. In the coupled systems, each neuron receives signals only via synaptic strength from the nearest neighbors. Based on the Lyapunov stability theory, the sufficient conditions for synchronization of the multiple systems with chaotic bursting behavior can be obtained. The synchronization condition about the control parameter g is also obtained by numerical method. Finally, numerical simulations are provided to show the effectiveness of the developed methods.

Chaotic synchronization of memristive neurons: Lyapunov function versus Hamilton function

“…The 2D Hindmarsh-Rose (HR) neuron model [3] is more than ten times faster in computational speed [5] than the HH model. It is capable of producing some important behaviors such as spiking and sub-threshold oscillations-which are also observed in real biological neurons-upon variations of the model's parameters [5][6][7]. To capture other dynamical behaviors, such as bursting and chaos, observed in real biological neurons, the original 2D HR neuron model has undergone few modifications.…”

Adaptive exponential lag synchronization for neural networks with mixed delays via intermittent control

“…In many practical situations, due to the finite transmission speed of signals, it is more reasonable to require the response system to synchronize with the drive system at a time lag rather than at exactly the same time [12][13][14][15]. For example, in a telephone communication system, the voice one hears on the receiver side at time t is the voice from the transmitter side at time t -τ [12,13].…”

“…Hence, time delays should be taken into account when exploring the dynamics of neural networks. In the light of these facts, many efforts have been made devoted to the study of lag synchronization of delayed chaotic systems and delayed neural networks in recent years [11][12][13][14][15][19][20][21][22][23]. For instance, the problem of lag synchronization control for memristor-based coupled delayed neural networks with parameter mismatches was explored in [11].…”

“…In order to guarantee synchronization between two chaotic systems can be realized, several control schemes have been proposed, such as feedback control, adaptive control, intermittent control and impulsive control [12][13][14][15][19][20][21][22][23][24][25][26][27][28][29][30][31][32]. Intermittent control, as a discontinuous control method, has been adopted in engineering fields in view of its convenient implementation in engineering control [33][34][35][36][37][38].…”

Synchronization of multiple bursting neurons ring coupled via impulsive variables

“…So, the issue of synchronization in complex dynamical networks has become a rather significant topic in both theoretical research and practical applications (see Refs. [6][7][8][9][10][11][12][13][14][15][16][17][18]).…”