Synchronization of delay bursting neuron system with stochastic noise via linear controllers

Shi, Xuerong; Han, Lixin; Wang, Zuolei; Tang, Keming

doi:10.1016/j.amc.2014.01.174

Cited by 5 publications

(4 citation statements)

References 30 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Remark 2 Compared with synchronization results in [10], [11], [12], [13], [14], and [15], there is no external control in the neuron (2).…”

Section: A Lyapunov Functionmentioning

confidence: 89%

“…Similar to master and slave synchronization of neural networks and chaotic systems [4], [5], [6], synchronization of two coupled HR neurons (master and slave neurons) has attracted increasing attention [7], [8], [9]. Several papers consider how to design the external control in one neuron, including linear feedback control, adaptive control, or other nonlinear control to achieve the synchronization of two coupled HR neurons [10], [11], [12], [13], [14], [15]. However, external control in one neuron may be very difficult even impossible to be realized [16] from the theory of neuroscience and molecular biology.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A new unidirectional coupling for global synchronization of two Hindmarsh-Rose neurons

Ding

Han

2015

The 27th Chinese Control and Decision Conference (2015 CCDC)

View full text Add to dashboard Cite

show abstract

“…Remark 2 Compared with synchronization results in [10], [11], [12], [13], [14], and [15], there is no external control in the neuron (2).…”

Section: A Lyapunov Functionmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

A new unidirectional coupling for global synchronization of two Hindmarsh-Rose neurons

Ding

Han

2015

The 27th Chinese Control and Decision Conference (2015 CCDC)

View full text Add to dashboard Cite

show abstract

“…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

{\overset{\overset{⁁}{y}}{true}}_{1} = {\overset{y}{true}}_{2},

{\overset{\overset{⁁}{y}}{true}}_{2} = {\overset{y}{true}}_{3} + v,

{\overset{\overset{⁁}{y}}{true}}_{3} = a_{1} (1 + ◃_{1}) {\overset{y}{true}}_{1} - a_{2} (1 + ◃_{2}) {\overset{y}{true}}_{2} - {\overset{y}{true}}_{3} - {\overset{y}{true}}_{1}^{3},

where

◃_{i} (i = 1, 2)

denotes the bounded uncertain parameters,

v = \ddot{x} - {\overset{y}{true}}_{3} + 2 x^{2} \dot{\overset{e}{true}} + x^{4} \overset{⁁}{e} + 2 x \dot{x} \overset{⁁}{e} + \overset{⁁}{e}

and

\overset{⁁}{e} = x - {\overset{y}{true}}_{1}

.…”

Section: Control Schemesmentioning

confidence: 99%

“…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 .…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2014

Self Cite

View full text Add to dashboard Cite

In this article, a partial synchronization scheme is proposed based on Lyapunov stability theory to track the signal of the delay hyperchaotic L€ u system using the Coullet system based on only one single controller. The proposed tracking control design has two advantages: only one controller is adopted in our approach and it can allow us to drive the hyperchaotic system to a simple chaotic system even with uncertain parameters. Numerical simulation results are given to demonstrate the effectiveness and robustness of the proposed partial synchronization scheme.

show abstract

Dynamics of three unidirectionally coupled autonomous Duffing oscillators and application to inchworm piezoelectric motors: Effects of the coupling coefficient and delay

Tchakui

Woafo

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

This work deals with the dynamics of three unidirectionally coupled Duffing oscillators and that of three coupled piezoelectric actuators, considering the special case of inchworm motors. Two configurations of the network are studied: ring configuration and chain configuration. The effects of the coupling coefficient and the time delay are analyzed through different bifurcation diagrams and phase difference variation. It is shown that varying the coupling coefficient and the time delay leads to the appearance of different dynamical behaviors: steady states, periodic and quasiperiodic oscillations, chaos, and phase synchronization.

show abstract

Synchronization of delay bursting neuron system with stochastic noise via linear controllers

Cited by 5 publications

References 30 publications

A new unidirectional coupling for global synchronization of two Hindmarsh-Rose neurons

A new unidirectional coupling for global synchronization of two Hindmarsh-Rose neurons

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

Dynamics of three unidirectionally coupled autonomous Duffing oscillators and application to inchworm piezoelectric motors: Effects of the coupling coefficient and delay

Contact Info

Product

Resources

About