Exponential stability of a class of competitive neural networks with multi-proportional delays

Zhou, Liqun; Zhao, Zhongying

doi:10.1007/s11063-015-9486-6

Cited by 24 publications

(7 citation statements)

References 29 publications

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“…Obviously, conditions (A 1 ) and (A 3 ) imply conditions (H 1 ) and (H 2 ), respectively, and Theorem II.1 does not require condition (A 2 ). So, our Theorem II.1 greatly improves theorem III.1 in [30].…”

Section: The Existence and Uniqueness Of Equilibrium Pointmentioning

confidence: 68%

“…Therefore, to study various dynamical behaviours of CNNs with proportional delays is of important theoretical and practical significants. But until now, there is only one published work dealing with the exponential stability of competitive neural networks with proportional delays. In , the authors discussed the exponential stability of CNNs with multi‐proportional delays of the form

\begin{matrix} right \{\begin{matrix} S T M : ε \frac{normald x_{i} false(t false)}{normald t} = - a_{i} x_{i} false(t false) + true \sum_{j = 1}^{n} b_{i j} f_{j} false(x_{j} false(t false) false) \\ + true \sum_{j = 1}^{n} c_{i j} f_{j} false(x_{j} false(q_{j} t false) false) + B_{i} true \sum_{j = 1}^{n} d_{j} m_{i j} false(t false) + I_{i}, \\ L T M : \frac{normald m_{i j} false(t false)}{normald t} = - m_{i j} false(t false) + d_{j} f_{i} false(x_{i} false(t false) false), \end{matrix} \end{matrix}

for t ≥ 1, i , j = 1,2,…, n , where x i ( t ) denotes the neuron current activity level; m i j is the synaptic efficiency; a i > 0 is the changing rate for neuron i ; b i j and c i j are constants which denote the strengths of connectivity between the cells j and i at time t and connection weights at time q j t respectively; d j is a given arbitrarily constant; q j is proportional delay factor and satisfies 0 < q j ≤ 1, q j t = t − (1 − q j ) t , in which (1 − q j ) t corresponds to the time delay function, and (1 − q j ) t → ∞ as q j ≠ 1, t → ∞ ;

q = \min_{1 \leq j \leq n} q_{j}; I_{i}

denotes the external input; B i > 0 is an external stimulus intensity; ε is a fast time scale decided by STM and ε > 0, f i (·) is the nonlinear activation function.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, to study various dynamical behaviours of CNNs with proportional delays is of important theoretical and practical significants. But until now, there is only one published work [30] dealing with the exponential stability of competitive neural networks with proportional delays. In [30], the authors discussed the exponential stability of CNNs with multi-proportional delays of the form…”

Section: Introductionmentioning

confidence: 99%

“…the authors of obtained sufficient conditions ensuring the existence, uniqueness and exponential stability of equilibrium points of .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

New Results on Exponential Stability of Competitive Neural Networks with Multi‐Proportional Delays

Qin

2018

Asian Journal of Control

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In this paper, we are concerned with a class of competitive neural networks with multi‐proportional delays. By applying the Banach fixed point theorem and constructing suitable Lyapunov functions, we obtain new sufficient conditions for the global exponential stability to this class of neural networks, which are easily verifiable. Finally, two examples are given to illustrate the effectiveness of the obtained results.

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Section: The Existence and Uniqueness Of Equilibrium Pointmentioning

confidence: 68%

\begin{matrix} right \{\begin{matrix} S T M : ε \frac{normald x_{i} false(t false)}{normald t} = - a_{i} x_{i} false(t false) + true \sum_{j = 1}^{n} b_{i j} f_{j} false(x_{j} false(t false) false) \\ + true \sum_{j = 1}^{n} c_{i j} f_{j} false(x_{j} false(q_{j} t false) false) + B_{i} true \sum_{j = 1}^{n} d_{j} m_{i j} false(t false) + I_{i}, \\ L T M : \frac{normald m_{i j} false(t false)}{normald t} = - m_{i j} false(t false) + d_{j} f_{i} false(x_{i} false(t false) false), \end{matrix} \end{matrix}

q = \min_{1 \leq j \leq n} q_{j}; I_{i}

denotes the external input; B i > 0 is an external stimulus intensity; ε is a fast time scale decided by STM and ε > 0, f i (·) is the nonlinear activation function.…”

Section: Introductionmentioning

confidence: 99%

“…Therefore, to study various dynamical behaviours of CNNs with proportional delays is of important theoretical and practical significants. But until now, there is only one published work [30] dealing with the exponential stability of competitive neural networks with proportional delays. In [30], the authors discussed the exponential stability of CNNs with multi-proportional delays of the form…”

Section: Introductionmentioning

confidence: 99%

“…the authors of obtained sufficient conditions ensuring the existence, uniqueness and exponential stability of equilibrium points of .…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

New Results on Exponential Stability of Competitive Neural Networks with Multi‐Proportional Delays

Qin

2018

Asian Journal of Control

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show abstract

“…It is worth mentioning that MCNNs with different time scales, which are extensions of conventional neural networks. It is a kind of unsupervised learning neural networks, which refers to the whole interconnection between input and output of the single layer neural networks [25]. MCNNs contain two types of state variables, including the aspects of long-term memory (LTM)and short-term memory(STM) [10], corresponding to the fast changes of the neural network states and the slow changes of the synapses by external stimuli, respectively.…”

mentioning

confidence: 99%

Synchronization for a class of complex-valued memristor-based competitive neural networks(CMCNNs) with different time scales

Zhao

Ren

2021

era

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In this paper, the synchronization problem of complex-valued memristive competitive neural networks(CMCNNs) with different time scales is investigated. Based on differential inclusions and inequality techniques, some novel sufficient conditions are derived to ensure synchronization of the driveresponse systems by designing a proper controller. Finally, a numerical example is provided to illustrate the usefulness and feasibility of our results.

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Global asymptotic stability and projective lag synchronization for uncertain inertial competitive neural networks

Chen

Wang

Tang

2023

Math Methods in App Sciences

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In this paper, the global asymptotic stability and projective lag synchronization of second‐order competitive neural networks with mixed time‐varying delays and uncertainties are studied without converting the original system into the usual first‐order system. Firstly, according to the Lyapunov functional method, inequality technique and the designed adaptive control strategy, the algebraic criteria of stability, and projective lag synchronization are derived by adjusting the control gain parameters in the controller. The obtained sufficient conditions are simple and easy to verify. Different from the traditional feedback controller, the adaptive controller can adjust its characteristics according to the system model, and external disturbance makes the system have better control performance. Besides, unlike the existing ones, this stability and synchronization problem is directly analyzed by constructing some new Lyapunov functionals with state variables and state variable derivatives. Finally, the effectiveness and practicability of the results are verified by numerical examples.

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Exponential stability of a class of competitive neural networks with multi-proportional delays

Cited by 24 publications

References 29 publications

New Results on Exponential Stability of Competitive Neural Networks with Multi‐Proportional Delays

New Results on Exponential Stability of Competitive Neural Networks with Multi‐Proportional Delays

Synchronization for a class of complex-valued memristor-based competitive neural networks(CMCNNs) with different time scales

Global asymptotic stability and projective lag synchronization for uncertain inertial competitive neural networks

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