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Published in: Neural Computing and Applications 2/2015

01-02-2015 | Original Article

Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments

Authors: Bingwen Liu, Cemil Tunç

Published in: Neural Computing and Applications | Issue 2/2015

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Abstract

In this paper, cellular neural networks with leakage delays and complex deviating arguments are considered. Some criteria are established for the existence of pseudo almost periodic solutions for this model by using the exponential dichotomy theory, contraction mapping fixed point theorem and inequality analysis technique. The results of this paper are new and complement previously known results.

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Literature
1.
go back to reference Rakkiyappan R, Balasubramaniam P (2010) On exponential stability results for fuzzy impulsive neural networks. Fuzzy Sets Syst 161(13):1823–1835CrossRefMATHMathSciNet Rakkiyappan R, Balasubramaniam P (2010) On exponential stability results for fuzzy impulsive neural networks. Fuzzy Sets Syst 161(13):1823–1835CrossRefMATHMathSciNet
2.
go back to reference Rakkiyappan R, Balasubramaniam P (2008) Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays. Appl Math Comput 198(2):526–533CrossRefMATHMathSciNet Rakkiyappan R, Balasubramaniam P (2008) Delay-dependent asymptotic stability for stochastic delayed recurrent neural networks with time varying delays. Appl Math Comput 198(2):526–533CrossRefMATHMathSciNet
3.
go back to reference Vembarasan V, Nagamani G, Balasubramaniam P, Park Ju H (2013) State estimation for delayed genetic regulatory networks based on passivity theory. Math Biosci 244(2):165–175CrossRefMATHMathSciNet Vembarasan V, Nagamani G, Balasubramaniam P, Park Ju H (2013) State estimation for delayed genetic regulatory networks based on passivity theory. Math Biosci 244(2):165–175CrossRefMATHMathSciNet
5.
go back to reference Peng GQ, Huang LH (2009) Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays. Nonlinear Anal Real World Appl 10(40):2434–2440CrossRefMATHMathSciNet Peng GQ, Huang LH (2009) Anti-periodic solutions for shunting inhibitory cellular neural networks with continuously distributed delays. Nonlinear Anal Real World Appl 10(40):2434–2440CrossRefMATHMathSciNet
6.
go back to reference Lu W, Chen T (2005) Global exponential stability of almost periodic solutions for a large class of delayed dynamical systems. Sci China Ser A Math 8(48):1015–1026CrossRef Lu W, Chen T (2005) Global exponential stability of almost periodic solutions for a large class of delayed dynamical systems. Sci China Ser A Math 8(48):1015–1026CrossRef
7.
go back to reference Huang Z, Mohamad S, Feng C (2010) New results on exponential attractivity of multiple almost periodic solutions of cellular neural networks with time-varying delays. Math Comput Model 52(9–10):1521–1531CrossRefMATHMathSciNet Huang Z, Mohamad S, Feng C (2010) New results on exponential attractivity of multiple almost periodic solutions of cellular neural networks with time-varying delays. Math Comput Model 52(9–10):1521–1531CrossRefMATHMathSciNet
8.
go back to reference Ammar B, Chérif F (2012) Existence and uniqueness of pseudo almost-periodic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Netw Learn Syst IEEE Trans 23:109–118CrossRef Ammar B, Chérif F (2012) Existence and uniqueness of pseudo almost-periodic solutions of recurrent neural networks with time-varying coefficients and mixed delays. Neural Netw Learn Syst IEEE Trans 23:109–118CrossRef
9.
go back to reference Ren Y, Li Y (2012) Stability and existence of periodic solutions for cellular neural networks with state dependent delays on time scales. Discrete Dyn Nat Soc 1–14. Art. ID 386706 Ren Y, Li Y (2012) Stability and existence of periodic solutions for cellular neural networks with state dependent delays on time scales. Discrete Dyn Nat Soc 1–14. Art. ID 386706
10.
go back to reference Gao J, Wang Q, Zhang L (2014) Existence and stability of almost-periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales. Appl Math Comput 237:639–649CrossRefMathSciNet Gao J, Wang Q, Zhang L (2014) Existence and stability of almost-periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales. Appl Math Comput 237:639–649CrossRefMathSciNet
12.
go back to reference Zhang H (2014) Existence and stability of almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Comput Appl 2014(24):1135–1146CrossRef Zhang H (2014) Existence and stability of almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Comput Appl 2014(24):1135–1146CrossRef
13.
go back to reference Zhang H, Shao J (2013) Existence and exponential stability of almost periodic solutions for CNNs with time-varying leakage delays. Neurocomputing 121(9):226–233CrossRef Zhang H, Shao J (2013) Existence and exponential stability of almost periodic solutions for CNNs with time-varying leakage delays. Neurocomputing 121(9):226–233CrossRef
14.
go back to reference Zhang H, Shao J (2013) Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms. Appl Math Comput 219(24):11471–11482CrossRefMathSciNet Zhang H, Shao J (2013) Almost periodic solutions for cellular neural networks with time-varying delays in leakage terms. Appl Math Comput 219(24):11471–11482CrossRefMathSciNet
15.
go back to reference 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):1–18 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):1–18
17.
go back to reference Liu B, Huang L (2007) Existence of periodic solutions for cellular neural networks with complex deviating arguments. Appl Math Lett 20:103–109CrossRefMATHMathSciNet Liu B, Huang L (2007) Existence of periodic solutions for cellular neural networks with complex deviating arguments. Appl Math Lett 20:103–109CrossRefMATHMathSciNet
18.
go back to reference Yang X, Li F, Long Y, Cui X (2010) Existence of periodic solution for discrete-time cellular neural networks with complex deviating arguments and impulses. J Frankl Inst 347:559–566CrossRefMATHMathSciNet Yang X, Li F, Long Y, Cui X (2010) Existence of periodic solution for discrete-time cellular neural networks with complex deviating arguments and impulses. J Frankl Inst 347:559–566CrossRefMATHMathSciNet
19.
go back to reference Hartung F, Krisztin T, Walther HO, Wu J (2006) Functional differential equations with state-dependent delays: theory and applications. In: Handbook of differential equations: ordinary differential equations, vol 3. Elsevier, Amsterdam, pp 435–545 Hartung F, Krisztin T, Walther HO, Wu J (2006) Functional differential equations with state-dependent delays: theory and applications. In: Handbook of differential equations: ordinary differential equations, vol 3. Elsevier, Amsterdam, pp 435–545
20.
go back to reference Zhang C (2003) Almost periodic type functions and ergodicity. Kluwer Academic/Science Press, BeijingCrossRefMATH Zhang C (2003) Almost periodic type functions and ergodicity. Kluwer Academic/Science Press, BeijingCrossRefMATH
22.
go back to reference Fink AM (1974) Almost periodic differential equations. In: Lecture notes mathematics, vol 377. Springer, Berlin, pp 80–112 Fink AM (1974) Almost periodic differential equations. In: Lecture notes mathematics, vol 377. Springer, Berlin, pp 80–112
23.
go back to reference Balasubramaniam P, Kalpana M, Rakkiyappan R (2011) Existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays. Circuits Syst Signal Process 30(6):1595–1616CrossRefMATHMathSciNet Balasubramaniam P, Kalpana M, Rakkiyappan R (2011) Existence and global asymptotic stability of fuzzy cellular neural networks with time delay in the leakage term and unbounded distributed delays. Circuits Syst Signal Process 30(6):1595–1616CrossRefMATHMathSciNet
24.
go back to reference Li X, Rakkiyappan R, Balasubramaniam P (2011) Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J Frankl Inst 348(2):135–155CrossRefMATHMathSciNet Li X, Rakkiyappan R, Balasubramaniam P (2011) Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations. J Frankl Inst 348(2):135–155CrossRefMATHMathSciNet
Metadata
Title
Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments
Authors
Bingwen Liu
Cemil Tunç
Publication date
01-02-2015
Publisher
Springer London
Published in
Neural Computing and Applications / Issue 2/2015
Print ISSN: 0941-0643
Electronic ISSN: 1433-3058
DOI
https://doi.org/10.1007/s00521-014-1732-8

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