Abstract
In this paper, based on the exponential dichotomy theory, contraction mapping fixed point theorem and inequality analysis technique, we obtain some sufficient conditions ensuring the existence and global exponential stability of pseudo almost periodic solutions for a new generalized cellular neural network model with continuously distributed leakage delays. Our results complement with some recent ones. Moreover, an illustrative example and its numerical simulation are given to demonstrate the effectiveness of the obtained results.
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Chua LO, Roska T (1990) Cellular neural networks with nonlinear and delay-type template elements. In: Proc. 1990 IEEE int. workshop on cellular neural networks and their applications, pp 12–25
Jiang H, Teng Z (2004) Global exponential stability of cellular neural networks with time-varying coefficients and delays. Neural Netw 17:1415–1425
Kwon O, Lee S, Park J (2010) Improved results on stability analysis of neuralnet works with time-varying delays: novel delay-dependent criteria. Mod Phys Lett B 24:775–789
Kwon O, Park J (2009) Exponential stability analysis for uncertain neural networks with interval time-varying delays. Appl Math Comput 212:530–541
Wu J (2001) Introduction to neural dynamics and signal trasmission delay. Walter de Gruyter, Belin
Park JH (2006) Further result on asymptotic stability criterion of cellular neural networks with time-varying discrete and distributed delays. Appl Math Comput 182:1661–1666
Li X, Ding C, Zhu Q (2010) Synchronization of stochastic perturbed chaotic neural networks with mixed delays. J Franklin Inst 347:1266–1280
Kwon O, Park J (2008) Delay-dependent stability for uncertain cellular neural networks with discrete and distribute time-varying delays. J Franklin Inst 345:766–778
Haykin S (1994) Neural networks. Prentice-Hall, Upper Saddle River
Kosok B (1992) Neural networks and fuzzy systems. Prentice-Hall, New Delhi
Gopalsamy K (1992) Stability and oscillations in delay differential equations of population dynamics. Kluwer Academic Publishers, Dordrecht
Gopalsamy K (2007) Leakage delays in BAM. J Math Anal Appl 325:1117–1132
Liu B (2013) Global exponential stability for BAM neural networks with time-varying delays in the leakage terms. Nonlinear Anal 14:559–566
Peng S (2010) Global attractive periodic solutions of BAM neural networks with continuously distributed delays in the leakage terms. Nonlinear Anal 11:2141–2151
Chen Z, Meng J (2012) Exponential convergence for cellular neural networks with time-varying delays in the leakage terms, Hindawi Publishing Corporation. Abstr Appl Anal 2012(941063):1–11
Chen Z, Yang M (2012) Exponential convergence for HRNNs with continuously distributed delays in the leakage terms. Neural Comput Appl. doi:10.1007/s00521-012-1172-2
Chen Z (2012) A shunting inhibitory cellular neural network with leakage delays and continuously distributed delays of neutral type. Neural Comput App. doi:10.1007/s00521-012-1200-2
Xiong W, Meng J (2013) Exponential convergence for cellular neural networks with continuously distributed delays in the leakage terms. Electron J Qual Theory Differ Equ 2013(10):1–12
Zhang C (2003) Almost periodic type functions and ergodicity. Kluwer Academic, Beijing
Fink AM (1974) Almost periodic differential equations. Lecture Notes in Mathematics, vol 377. Springer, Berlin
Chérif Farouk (2012) Existence and global exponential stability of pseudo almost periodic solution for SICNNs with mixed delays. J Appl Math Comput 39:235–251
Zhou T, Liu Y, Chen A (2006) Almost periodic solution for shunting inhibitory cellular neural networks with time-varying delays and variable coefficients. Neural Process Lett 23(3):243–255
Li Y, Wang C, Li X (2013) Existence and global exponential stability of almost periodic solution for high-order BAM neural networks with delays on time scales. Neural Process Lett. doi:10.1007/s11063-013-9302-0
Zhang H, Shao J (2013) Existence and exponential stability of almost periodic solutions for CNNs with time-varying leakage delays. Neurocomputing 121(9):226–233
Zhang H, Shao J (2013) Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms. Appl Math Comput 219(24):11471–11482
Zhang H (2014) Existence and stability of almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Comput Appl 2014(24):1135–1146
Liu B (2014) Global exponential stability of positive periodic solutions for a delayed Nicholson’s blowflies model. J Math Anal Appl 412:212–221
Meng J (2013) Global exponential stability of positive pseudo almost periodic solutions for a model of hematopoiesis. Abstr Appl Anal 2013(463076):1–11
Wang W, Liu B (2014) Global exponential stability of pseudo almost periodic solutions for SICNNs with time-varying leakage delays. Abstr Appl Anal 2014(967328):1–17
Li L, Fang Z, Yang Y (2012) A shunting inhibitory cellular neural network with continuously distributed delays of neutral type. Nonlinear Anal Real World Appl 13:1186–1196
Acknowledgments
The author would like to express the sincere appreciation to the editor and reviewers for their helpful comments in improving the presentation and quality of the paper. This work was supported by the construct program of the key discipline in Hunan province (Mechanical Design and Theory), the Scientific Research Fund of Hunan Provincial Natural Science Foundation of PR China (Grant No. 11JJ6006), and the Natural Scientific Research Fund of Hunan Provincial Education Department of PR China (Grants No. 11C0916, 11C0915).
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Liu, B. Pseudo Almost Periodic Solutions for CNNs with Continuously Distributed Leakage Delays. Neural Process Lett 42, 233–256 (2015). https://doi.org/10.1007/s11063-014-9354-9
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DOI: https://doi.org/10.1007/s11063-014-9354-9
Keywords
- Cellular neural networks
- Pseudo almost periodic solution
- Exponential stability
- Continuously distributed leakage delay