2014
DOI: 10.1016/j.amc.2014.04.078
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Existence and global asymptotic stability of positive periodic solution of delayed Cohen–Grossberg neural networks

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Cited by 22 publications
(9 citation statements)
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“…It follows that y D .y 1 , : : : , y n / T maps D OE k 1 , k 1 OE k 2 , k 2 OE k n , k n into itself. Therefore, by Brower's fixed point theorem, y has at least one equilibrium point for system (1). This completes the proof.…”
Section: Proofsupporting
confidence: 57%
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“…It follows that y D .y 1 , : : : , y n / T maps D OE k 1 , k 1 OE k 2 , k 2 OE k n , k n into itself. Therefore, by Brower's fixed point theorem, y has at least one equilibrium point for system (1). This completes the proof.…”
Section: Proofsupporting
confidence: 57%
“…The activation function g j .x j .t// denotes the output of the j th neuron at time t. y i .t/ is the output, and a ij , b ij and c ij are the connection weights of the neural networks, respectively. In the neural network (1), the bounded functions .t/ and ı.t/ represent the discrete and distributed time-varying delays with 0 Ä .t/ Ä , P .t/ Ä and 0 Ä ı.t/ Ä ı.…”
Section: Notations and Preliminary Resultsmentioning
confidence: 99%
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“…}, the fixed impulsive moments t k satisfy t k−1 < t k and lim k→+∞ t k = +∞, δ(t) is the Dirac impulsive function, which means that the state of network (1) has jumps at t k for k ∈ N. u jk and w jk represent the strength of impulsive effects of the jth neuron at time t k and t k − τ (t), respectively. If u jk = w jk = 0, then model (1) becomes continuous neural network models (see [2,18,19]). …”
Section: Preliminariesmentioning
confidence: 99%
“…Meanwhile, network (16) is globally uniformly exponentially convergent to the ball (19). λ > 0 is a unique solution of the equality λ = a − be λτ and λ m = min 1≤i≤n {p i }.…”
Section: Theoremmentioning
confidence: 99%