Impulsive synchronization of time delay bursting neuron systems with unidirectional coupling

Wang, Zuolei; Jiang, Yao‐Lin; Liu, Hongli

doi:10.1002/cplx.21576

Cited by 13 publications

(11 citation statements)

References 57 publications

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“…For any chaotic system, the bounds of state variables can be obtained. Therefore, the bound of state variable y 1 ( t ) of chaotic HR neuron can be used. Remark In and , the nonlinear control methods were used to derive synchronization criteria. For Proposition 1 of this article, we only use the linear feedback control to achieve synchronization for two HR neurons.…”

Section: Master–slave Synchronization Criteriamentioning

confidence: 99%

“…Moreover, the synchronization of HR neurons is achieved by the linear feedback control

u (t) = true(\begin{matrix} 1.36 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{matrix} true) e (t)

for the example . However, the nonlinear control methods were used to achieve the synchronization for neurons in . Example Consider the following HR model

true{\begin{array}{l} {\dot{y}}_{1} (t) = - y_{1}^{2} (t) - y_{1}^{3} (t) + y_{2} (t) - y_{3} (t) + 3.2, \\ {\dot{y}}_{2} (t) = 1 - \sqrt{3} y_{1}^{2} (t) - y_{2} (t), \\ {\dot{y}}_{3} (t) = 0.76 (y_{1} (t) + 1.56) - 0.006 y_{3} (t), \end{array}

with the initial condition

y_{1_{0}} = 0.7

and

y_{2_{0}} = 0.3, y_{3_{0}} = 0.4

. The chaotic attractor can be illustrated by Figure which reveals that

- 2.5 = - m_{1} \leq y_{1} (t) \leq 1.04 = m_{2}

.…”

Section: Examplesmentioning

confidence: 99%

“…Checco et al studied the synchronization of networks of HR neurons but some local synchronization criteria were derived. Che et al , Chen et al , Nguyen and Hong , Nguyen and Hong , Wang and Shi , Wang et al investigated synchronization of chaotic neurons and derived synchronization criteria by using nonlinear control methods. Undoubtedly, the linear feedback control is easier to be implemented than the nonlinear control.…”

Section: Introductionmentioning

confidence: 99%

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Master–slave synchronization criteria for chaotic hindmarsh–rose neurons using linear feedback control

Ding

Han

2015

Complexity

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Section: Master–slave Synchronization Criteriamentioning

confidence: 99%

“…Moreover, the synchronization of HR neurons is achieved by the linear feedback control

u (t) = true(\begin{matrix} 1.36 & 0 & 0 \\ 0 & 0 & 0 \\ 0 & 0 & 0 \end{matrix} true) e (t)

for the example . However, the nonlinear control methods were used to achieve the synchronization for neurons in . Example Consider the following HR model

true{\begin{array}{l} {\dot{y}}_{1} (t) = - y_{1}^{2} (t) - y_{1}^{3} (t) + y_{2} (t) - y_{3} (t) + 3.2, \\ {\dot{y}}_{2} (t) = 1 - \sqrt{3} y_{1}^{2} (t) - y_{2} (t), \\ {\dot{y}}_{3} (t) = 0.76 (y_{1} (t) + 1.56) - 0.006 y_{3} (t), \end{array}

with the initial condition

y_{1_{0}} = 0.7

and

y_{2_{0}} = 0.3, y_{3_{0}} = 0.4

. The chaotic attractor can be illustrated by Figure which reveals that

- 2.5 = - m_{1} \leq y_{1} (t) \leq 1.04 = m_{2}

.…”

Section: Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Master–slave synchronization criteria for chaotic hindmarsh–rose neurons using linear feedback control

Ding

Han

2015

Complexity

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“…For impulsive synchronization, most of the approaches in the literature assume that the parameters of chaotic system are known exactly [15][16][17][18][19][20][21]. Unfortunately, due to the complexity and uncertainty of chaotic system, it is not always feasible to obtain the knowledge of parameters in some practical cases.…”

Section: Introductionmentioning

confidence: 99%

Adaptive impulsive synchronization of uncertain delayed chaotic system with full unknown parameters via discrete‐time drive signals

Gao

Cheng

2014

Complexity

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This article investigates the adaptive impulsive synchronization of delayed chaotic system with full unknown parameters. Aiming at this problem, we propose a new adaptive strategy, in which both the adaptive-impulsive controller and the parameters adaptive laws are designed via the discrete-time signals from the drive system. The corresponding theoretical proof is given to guarantee the effectiveness of the proposed strategy. Moreover, the concrete adaptive strategies are achieved for delayed Hopfield neural network, optical Ikeda system and the wellknown delayed L€ u chaotic system. As expected, numerical simulations show the effectiveness of the proposed strategy. This method has potential applications in parameters estimation, secure communication, and cryptanalysis when only discrete signals are transmitted in communication channel. FIGURE 7Curves of parameters estimationr 1 ðtÞ,r 2 ðtÞ, andã 3 ðtÞ.

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“…Nowadays, different techniques and methods have been put forward to achieve chaos synchronization, for instance, the PC synchronization method , linear and nonlinear feedback synchronization method , impulsive synchronization method , tracking synchronization method , among many others . The tracking synchronization method is about the use of control laws to achieve the synchronization between nonlinear oscillators with different structures and orders, where the variable states of the slave system are forced to follow the trajectories of the master system.…”

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

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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.

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Impulsive synchronization of time delay bursting neuron systems with unidirectional coupling

Cited by 13 publications

References 57 publications

Master–slave synchronization criteria for chaotic hindmarsh–rose neurons using linear feedback control

Master–slave synchronization criteria for chaotic hindmarsh–rose neurons using linear feedback control

Adaptive impulsive synchronization of uncertain delayed chaotic system with full unknown parameters via discrete‐time drive signals

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

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