Exponential input-to-state stability of stochastic Cohen–Grossberg neural networks with mixed delays

Zhu, Quanxin; Cao, Jinde; Rakkiyappan, R.

doi:10.1007/s11071-014-1725-2

Cited by 200 publications

(74 citation statements)

References 39 publications

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“…So the abnormal synchronization neural networks (2) multilags synchronize under adaptive periodical intermittent controllers (8) and updating laws (9). This completes the proof of Theorem 5.…”

Section: Mathematical Problems In Engineeringsupporting

confidence: 64%

“…The parameters are set as = 1, ℎ = 0.4. According to Theorem 5, it is found that (11) is satisfied under the adaptive periodically intermittent controllers (8) and corresponding updating laws (9). The time series of the pathological neural network (2) by adaptive periodically intermittent controllers are numerically demonstrated as in Figure 5.…”

Section: Simulationmentioning

confidence: 97%

“…where = ‖Γ‖ 2 , > 0 is the smallest real root of the equation 1 − − ( 2 2 / )exp{ } = 0, then the abnormal synchronization neural networks (2) multilag synchronization is under adaptive periodical intermittent controllers (8) and updating laws (9).…”

Section: Theoremmentioning

confidence: 99%

“…It is reported that epileptic seizures, diffusion, and holding out are mostly due to the reciprocity of neuron network in the brain with functional connectivity with small world network characteristic [6][7][8][9]. If we can fully understand the functional connectivity of brain with epileptic seizures by complex network analysis methods, then, we will offer a new research approach for epileptic seizure prediction or controlling.…”

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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Section: Mathematical Problems In Engineeringsupporting

confidence: 64%

Section: Simulationmentioning

confidence: 97%

Section: Theoremmentioning

confidence: 99%

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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“…Many scholars have devoted themselves into the dynamics analysis of neural networks with various types of time delays and many valuable results have been achieved in the existing literature see [18][19][20][21][22][23][24][25][26]. There are three typical types of time delays for incorporating time delays into neural networks: (i) introduce transmission delays into the neural 2 Complexity networks, and consider discrete delays, distributed delays, mixed delays, even state depended delays, or complex delays; (ii) consider the delays in the leakage term; (iii) take into account neutral type delays.…”

Section: Introductionmentioning

confidence: 99%

Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales

Meng

2017

Complexity

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We propose a class of neutral type quaternion-valued neural networks with delays in the leakage term on time scales that can unify the discrete-time and the continuous-time neural networks. In order to avoid the difficulty brought by the noncommutativity of quaternion multiplication, we first decompose the quaternion-valued system into four real-valued systems. Then, by applying the exponential dichotomic theory of linear dynamic equations on time scales, Banach's fixed point theorem, the theory of calculus on time scales, and inequality techniques, we obtain some sufficient conditions on the existence and global exponential stability of pseudo almost periodic solutions for this class of neural networks. Our results are completely new even for both the case of the neural networks governed by differential equations and the case of the neural networks governed by difference equations and show that, under a simple condition, the continuous-time quaternion-valued network and its corresponding discrete-time quaternionvalued network have the same dynamical behavior for the pseudo almost periodicity. Finally, a numerical example is given to illustrate the feasibility of our results.

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Synchronization of stochastic memristive neural networks via event‐triggered impulsive control

Zhang,

Mu,

2023

Adaptive Control & Signal

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This paper investigates the synchronization problem for master‐slave stochastic memristive neural networks (SMNNs) with time‐delay via event‐triggered impulsive control (ETIC). Firstly, a novel ETIC method is designed for SMNNs to realize quasi‐synchronization in mean square sense. Different from time‐triggered impulsive control (TTIC) in the existing results on SMNNs, the proposed event‐triggered method determines impulsive instants based on the real‐time system states, which can reduce redundant impulses. Compared with the existing ETIC for deterministic memristive neural networks (MNNs), the proposed event‐triggered mechanism (ETM) can exclude Zeno behavior completely by adding the waiting time, when stochastic disturbances occur in MNNs. Secondly, if the master SMNNs have nonzero control inputs, an adaptive‐impulsive hybrid controller with ETM is designed to realize almost surely exponential synchronization. Under the ETM, the number of transmitted events is reduced, then control resources can be saved. Zeno behavior can be excluded in almost sure sense. Ultimately, simulations are presented to illustrate the validity of the obtained results.

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Exponential input-to-state stability of stochastic Cohen–Grossberg neural networks with mixed delays

Cited by 200 publications

References 39 publications

The Controller Design of the Epilepsy Therapy Apparatus

The Controller Design of the Epilepsy Therapy Apparatus

Existence and Global Exponential Stability of Pseudo Almost Periodic Solutions for Neutral Type Quaternion-Valued Neural Networks with Delays in the Leakage Term on Time Scales

Synchronization of stochastic memristive neural networks via event‐triggered impulsive control

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