2007
DOI: 10.1016/j.camwa.2007.01.005
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Existence and exponential stability of periodic solutions for a class of Cohen–Grossberg neural networks with bounded and unbounded delays

Abstract: This paper is concerned with existence and global exponential stability of periodic solutions for a class of Cohen-Grossberg neural networks with bounded and unbounded delays. By the continuation theorem of coincidence degree theory and differential inequality techniques, we deduce some sufficient conditions ensuring existence as well as global exponential stability of periodic solution. These conditions in our results are milder and less restrictive than that of previous known criteria since the hypothesis of… Show more

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Cited by 13 publications
(5 citation statements)
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“…Remark 14. Recently, the global exponential stability of periodic or almost periodic solution to CGNNs is studied by many scholars (see [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]). However, few authors pay attention to the global uniform asymptotic stability.…”
Section: The Global Uniform Asymptotic Stability Of Pseudo Almost Permentioning
confidence: 99%
See 1 more Smart Citation
“…Remark 14. Recently, the global exponential stability of periodic or almost periodic solution to CGNNs is studied by many scholars (see [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]). However, few authors pay attention to the global uniform asymptotic stability.…”
Section: The Global Uniform Asymptotic Stability Of Pseudo Almost Permentioning
confidence: 99%
“…Some attractivity and asymptotic stability results have also been published [3,[11][12][13][14]. Many authors specially devote themselves to study the existence and global exponential stability of periodic or almost periodic solution to CGNNs [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30]; for the other dynamic properties, see also the literatures [31,32]. However, to the best of our knowledge, few authors have discussed the existence and the global uniform asymptotic stability of pseudo almost periodic solutions to CGNNs.…”
Section: Introductionmentioning
confidence: 99%
“…In 1989, Marcus and Westervelt [22] introduced for the first time a discrete delay in the Hopfield model (1.2), and they observed that the delay can destabilize the system. In fact, the delays can affect the dynamic behavior of neural network models [3,22] and, for this reason, stability of delayed neural network models has been investigated extensively (see [1,2,4,6,7,9,11,18,19,20,23,25,26,27,28,29,30], and the references therein). Another relevant fact to take into account is that the neuron charging time, the interconnection weights, and the external inputs often change as time proceeds.…”
Section: Introductionmentioning
confidence: 99%
“…For neural network models with time-varying coefficients, many authors derive sufficient conditions ensuring that all solutions converge exponentially to zero or to an equilibrium point [9,19,30]. Other authors assume periodic, or almost periodic, coefficient functions and derive sufficient conditions ensuring the existence of a periodic, or almost periodic, solution and its global exponential stability [7,18,20,26,27]. We should say that, in the significative recent research papers [1,2], the authors consider neural network models with weighted pseudo-almost automorphic coefficients and general conditions are assumed to prove the existence and global exponential stability of a weighted pseudoalmost automorphic solution.…”
Section: Introductionmentioning
confidence: 99%
“…The applicability and efficiency of such networks hinge upon their dynamics, and therefore the investigation of dynamical behaviors is a preliminary step for any practical design and application of the networks. Recently, considerable effort has been devoted to the study of dynamic behaviors on the existence and stability of the equilibrium point, periodic and almost periodic solutions of SICNNs with time-varying delays and continuously distributed delays (see [5,14,19,27,35]). …”
Section: Introductionmentioning
confidence: 99%