Synchronization of multiple bursting neurons ring coupled via impulsive variables

Abstract

Synchronization behavior of bursting neurons is investigated in a neuronal network ring impulsively coupled, in which each neuron exhibits chaotic bursting behavior. Based on the Lyapunov stability theory and impulsive control theory, sufficient conditions for synchronization of the multiple systems coupled with impulsive variables can be obtained. The neurons become synchronous via suitable impulsive strength and resetting period. Furthermore, the result is obtained that synchronization among neurons is weakened with the increasing of the reset period and the number of neurons. Finally, numerical simulations are provided to show the effectiveness of the theoretical results.© 2014 Wiley Periodicals, Inc. Complexity 21: 29–37, 2015

Tracking the state of the delay hyperchaotic Lü system using the coullet chaotic system via a single controller

“…It is well known that in practical applications chaotic systems are unavoidably affected by external disturbance, like noise , variations of parameters , and so on . In this case, the slaved Coullet chaotic system with some uncertain parameters is considered as where denotes the bounded uncertain parameters, and .…”

“…But Pecora and Carroll (PC) found a control method to successfully keep two chaotic systems synchronous. Ever since PC's original research work, there has been considerable work on chaos synchronization and its practical applications in secure communication , complex networks , biotic science , and so on .…”

Robust Adaptive Synchronization of Ring Configured Uncertain Chaotic FitzHugh–Nagumo Neurons under Direction-Dependent Coupling

“…In a neuronal network, a large number of neurons are inter-connected in various fashions under multifarious coupling phenomena. Recently, the studies on the dynamical behavior of a single neuron, a collective behavior of coupled neurons, and synchronization among the neurons have been extensively investigated (Thompson et al, 1999 ; Hua and Smith, 2004 ; Zhang et al, 2006 ; Wu and Chen, 2008 ; Yu et al, 2013 ; Wang et al, 2015 ). Synchronization of neurons plays a key role in the transmission process of neuronal signals, and enables effective communications in the brain or to the muscles (Knoblauch and Palm, 2005 ; Wang et al, 2008a , b ; Nguyen and Hong, 2011 , 2013 ).…”

“…To a certain extent, efforts have been dedicated to the study of the dynamics of the neuronal networks coupled in a ring fashion, specifically by exploiting the impact of time delays (Campbell et al, 2005 ; Xu, 2008 ; Song and Xu, 2012 ; Zhang, 2014 ; Wang et al, 2015 ; Mao and Wang, 2016 ; Yuan et al, 2016 ; Mao, 2017 ). A recent work by Zhou et al ( 2009 ) extended the synchronization problem to a network of coupled FHN neurons and explored the impact of the gap junctions on the network.…”

Synchronization of Neuronal Circuits with Ring Connection on PSpice

“…Based on the proposed neuron models, the dynamical properties of single neuron, collective behaviors of neurons, and transition of neuronal electric activities have been investigated extensively [4][5][6][7]. For example, synchronization between electric activities of neurons [8][9][10], phase synchronization [11,12], coherence resonance [13][14][15][16][17][18], transition of electric modes in neurons [19][20][21][22][23][24], and the development and transition of spatial pattern in neuronal networks [25][26][27][28][29] have been discussed in numerical studies. In a biological experimental way, isolated neurons can be immersed into certain ionic liquid to detect the effect of external forcing from potassium, sodium, and even the leakage current [30][31][32].…”