Abstract
This paper is concerned with the generalized neutral-type neural networks with impulses and delays. By applying the contraction mapping principle and generalized Gronwall–Bellman’s inequality, we employ a novel argument to establish new results on the existence, uniqueness and exponential stability of piecewise pseudo almost periodic solutions. Some corresponding results in the literature can be enriched and extended. Moreover, a numerical example is given to illustrate the effectiveness of our results.
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.References
Alonso AI, Hong J, Rojo J (1998) A class of ergodic solutions of differential equations with piecewise constant arguments. Dyn Syst Appl 7:561–574
Gui ZJ, Ge WG, Yang XS (2007) Periodic oscillation for a Hopfield neural networks with neutral delays. Phys Lett A 364:267–273
Hale J (1977) Theory of functional differential equations. Springer, New York
Kong FC (2017) Positive piecewise pseudo-almost periodic solutions of first-order singular differential equations with impulses. J Fixed Point Theory Appl. https://doi.org/10.1007/s11784-017-0438-9.
Lakshmikantham V, Bainov DD, Simeonov PS (1989) Theory of impulse differential equations. World Scientific, Singapore
Liu YR, Wang ZD, Liu XH (2012) Stability analysis for a class of neutral-type neural networks with Markovian jumping parameters and mode-dependent mixed delays. Neurocomputing 94:46–53
Liu J, Zhang C (2013) Composition of piecewise pseudo almost periodic functions and applications to abstract impulsive differential equations. Adv Differ Equ 11:1–21
Liu DY, Du Y (2015) New results of stability analysis for a class of neutral-type neural network with mixed time delays. Int J Mach Learn Cybern 6(4):555–566
Li XD, O’Regan D, Akca H (2015) Global exponential stabilization of impulsive neural networks with unbounded continuously distributed delays. IMA J Appl Math 80(1):85–99
Liu BW (2015) Pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays. Neurocomputing 148:445–454
Liu BW (2015) Pseudo almost periodic solutions for CNNs with continuously distributed leakage delays. Neural Process Lett 42:233–256
Liu BW, Tunç C (2015) Pseudo almost periodic solutions for CNNs with leakage delays and complex deviating arguments. Neural Comput Appl 26:429–435
Liu C, Liu WP, Yang Z (2016) Stability of neural networks with delay and variable-time impulses. Neurocomputing 171:1644–1654
Li YK, Yang L, Li B (2016) Existence and stability of pseudo almost periodic solution for neutral type high-order hopfield neural networks with delays in leakage terms on time scales. Neural Process Lett 44(3):603–623
Rakkiyappan R, Balasubramaniam P (2008) New global exponential stability results for neutral type neural networks with distributed time delays. Neurocomputing 71:1039–1045
Rakkiyappan R, Balasubramaniam P (2008) LMI conditions for global asymptotic stability results for neutral-type neural networks with distributed time delays. Appl Math Comput 204(1):317–324
Samoilenko AM, Perestyuk NA (1995) Impulsive differential equations. World Scientific Publishing Corporation, Singapore
Samli R, Arik S (2009) New results for global stability of a class of neutral-type neural systems with time delays. Appl Math Comput 210(2):564–570
Stamov GT (2012) Almost periodic solutions of impulsive differential equations. Springer, Berlin
Wang K, Zhu YL (2010) Stability of almost periodic solution for a generalized neutral-type neural networks with delays. Neurocomputing 73(16):3300–3307
Wang XH, Li SY, Xu DY (2011) Globally exponential stability of periodic solutions for impulsive neutral-type neural networks with delays. Nonlinear Dyn 64(1):65–75
Wang C, Agarwal RP (2014) Weighted piecewise pseudo almost automorphic functions with applications to abstract impulsive \(\nabla \)-dynamic equations on time scales. Adv Differ Equ 2014:153
Wang C (2016) Piecewise pseudo almost periodic solution for impulsive non-autonomous high-order Hopfield neural networks with variable delays. Neurocomputing 171:1291–1301
Xu CJ, Zhang QM, Wu YS (2014) Existence and stability of pseudo almost periodic solutions for shunting inhibitory cellular neural networks with neutral type delays and time-varying leakage delays. Netw Comput Neural 25(4):168–192
Xie D, Jiang YP (2016) Global exponential stability of periodic solution for delayed complex-valued neural networks with impulses. Neurocomputing 207:528–538
Yang CB, Huang TZ (2013) New results on stability for a class of neural networks with distributed delays and impulses. Neurocomputing 111:115–121
Zhang J, Gui ZJ (2009) Periodic solutions of nonautonomous cellular neural networks with impulses and delays. Nonlinear Anal Real World Appl 10(3):1891–1903
Zhao DL, Han D (2011) Stability of linear neutral differential equations with delays and impulses established by the fixed points method. Nonlinear Anal 74(18):7240–7251
Zheng CD, Wang Y, Wang ZS (2014) New stability results of neutral-type neural networks with continuously distributed delays and impulses. Int J Comput Math 91(9):1880–1896
Zhang CY (2003) Almost periodic type functions and ergodicity. Kluwer Academic/Science Press, Beijing
Zhang CY (1995) Pseudo almost periodic solutions of some differential equations II. J Math Anal Appl 192:543–561
Zhang CY (1994) Pseudo almost periodic solutions of some differential equations. J Math Anal Appl 151:62–76
Zhou QY (2016) Pseudo almost periodic solutions for SICNNs with leakage delays and complex deviating arguments. Neural Process Lett 44(2):375–386
Acknowledgements
The authors thank the anonymous reviewers for their insightful suggestions which improved this work significantly. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11471109, 11471278).
Funding was provided by Scientific Research Fund of Hunan Provincial Education Department (Grant No. 13A093).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Kong, F., Luo, Z. & Wang, X. Piecewise Pseudo Almost Periodic Solutions of Generalized Neutral-Type Neural Networks with Impulses and Delays. Neural Process Lett 48, 1611–1631 (2018). https://doi.org/10.1007/s11063-017-9758-4
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11063-017-9758-4
Keywords
- Neutral-type neural networks
- Contraction mapping principle
- Gronwall–Bellman’s inequality
- Exponential stability
- Impulses
- Delays