Projective lag synchronization of Markovian jumping neural networks with mode-dependent mixed time-delays based on an integral sliding mode controller

Ma, Yuechao; Zheng, Yuqing

doi:10.1016/j.neucom.2015.05.062

Cited by 15 publications

(5 citation statements)

References 48 publications

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“…which contradicts the second inequality in (25). Hence Δ( ) < 0 holds; that is, for ∈ [ℎ, ), we have…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 89%

“…Particularly, the research of synchronization of coupled neural networks is an important step for understanding brain science and designing coupled neural networks for practical use. Many control techniques, such as linear feedback control [14][15][16], adaptive feedback 2 Mathematical Problems in Engineering control [17,18], stochastic control [19,20], impulsive control [21,22], pinning control [21][22][23][24], finite-time control [25][26][27], sliding mode control [28,29], and intermittent control [30,31], have been developed to drive the synchronization of networks.…”

Section: Introductionmentioning

confidence: 99%

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The Controller Design of the Epilepsy Therapy Apparatus

Sun

Zhang

2017

Mathematical Problems in Engineering

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Deep brain stimulation (DBS) is one of the effective treatments of epilepsy. Based on the Lyapunov stability theory combined with the method of the periodically intermittent control and adaptive control, the abnormal synchronization neural network models with high frequency oscillation are achieved with multilag synchronization in this paper. Some simple criteria are derived for the multilag synchronization of the coupled neural networks with coupling delays. The adaptive periodically intermittent control which we have obtained can cut down control cost. The sufficient conditions of this paper for abnormal neural network multilag synchronization are less conservative and can be applied in a wider area. Finally, simulation results show the effectiveness of the proposed control strategy. The design of controllers and control strategy may provide a potential electrical stimulation therapy on neurological diseases caused by abnormal synchronization. And they can provide technical support for epilepsy treatment apparatus research and development.

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“…which contradicts the second inequality in (25). Hence Δ( ) < 0 holds; that is, for ∈ [ℎ, ), we have…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 89%

Section: Introductionmentioning

confidence: 99%

The Controller Design of the Epilepsy Therapy Apparatus

Sun

Zhang

2017

Mathematical Problems in Engineering

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show abstract

“…Using the control mechanisms in the neural population is a practical approach to modulate seizure activity which is considered by the researchers. Among various types of control strategies [7,8,9], neurons phase distribution control [4,10] is one of the suitable options because it has remarkable features; for instance, in this method, this control takes the analysis of high-dimensional systems more tractable, which reduces the time of solving the problems and improves the performance of the control. It also optimizes the energy consumed by defining a proportional control.…”

Section: Introductionmentioning

confidence: 99%

NPDS toolbox: Neural population (De) synchronization toolbox for MATLAB

et al. 2022

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“…Several works on projective-lag synchronization have been released in continuous-time chaotic systems (Almahbashi et al, 2016; Feng et al, 2013; Hoang and Nakagawa, 2008; Ma and Zheng, 2015; Wu and Lu, 2012). However, there are few results about projective-lag synchronization in discrete-time chaotic systems.…”

Section: Introductionmentioning

confidence: 99%

A general method for projective-lag synchronization of heterogeneous chaotic maps with different dimensions

Feng

Yang

Zhou

2021

Journal of Vibration and Control

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Projective-lag synchronization of complex systems has attracted much attention in the past two decades. However, the majority of previous studies concentrated on continuous-time chaotic systems or discrete-time chaotic systems with the same dimensions. In our present study, a general method for projective-lag synchronization of different discrete-time chaotic systems characterized with different dimensions is first demonstrated. On the basis of stability theory of discrete-time dynamical systems and Lyapunov stability theory, general controllers are designed by using the active control method. The method could achieve projective-lag synchronization in both cases: [Formula: see text] and [Formula: see text]. The effectiveness and feasibility of the proposed method is demonstrated by the projective-lag synchronization between two-dimensional Lorenz discrete-time system and three-dimensional Stefanski map, as well as between the three-dimensional generalized Hénon map and the two-dimensional quadratic map, respectively.

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Projective lag synchronization of Markovian jumping neural networks with mode-dependent mixed time-delays based on an integral sliding mode controller

Cited by 15 publications

References 48 publications

The Controller Design of the Epilepsy Therapy Apparatus

The Controller Design of the Epilepsy Therapy Apparatus

NPDS toolbox: Neural population (De) synchronization toolbox for MATLAB

A general method for projective-lag synchronization of heterogeneous chaotic maps with different dimensions

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