Exponential stability of periodic solution for a memristor-based inertial neural network with time delays
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In this paper, exponential stability of periodic solution for an inertial neural network is studied. Different from most research on inertial neural networks, the model in this paper is based on memristors and is involved with periodic solutions. In order to simplify the difficulty in dealing with inertial terms and constructing Lyapunov functions, the inertial neural network in this paper is transformed into a suitable neural network with enhanced characteristics by using appropriate variable transformation method. Under the Lyapunov stability theory and Leary-Schauder alternative theorem, we prove the existence and global exponential stability of the periodic solution for the inertial neural network under mild conditions. At last, the feasibility of the theoretical conclusions is illustrated by some numerical examples.
KeywordsMemristor-based inertial neural network Leary-Schauder alternative theorem Periodic solutions Global exponential stability
This research is supported by the National Science Foundation of China (61773136, 11471088).
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Conflict of interest statement
We declare that we have no financial and personal relationships with other people or organizations that can inappropriately influence our work, there is no professional or other personal interest of any nature or kind in any product, service and/or company that could be construed as influencing the position presented in, or the review of, the manuscript entitled “Exponential Stability of Periodic Solution for a Memristor-based Inertial Neural Network with Time Delays.”
- 14.Jia Q, Tang WKS (2018) Consensus of multi-agents with event-based nonlinear coupling over time-varying digraphs. In: IEEE transactions on circuits and systems II express briefs. vol 99, pp 1–1Google Scholar
- 16.Lakshmanan S, Prakash M, Lim, CP, Rakkiyappan R, Balasubramaniam P, Nahavandi S (2016) Synchronization of an inertial neural network with time-varying delays and its application to secure communication. In: IEEE transactions on neural networks and learning systems. vol 99, pp 1–13Google Scholar
- 18.Li SJ, Szulkin A (2013) Periodic solutions for a class of nonautonomous hamiltonian systems. Nonlinear Anal Theor Methods Appl 61(8):1413–1426Google Scholar
- 36.Yang L, Jie Y, Yuan H, Xu L, Li S, Man Q (2015) Mapreduce based parallel neural networks in enabling large scale machine learning. Comput Intell Neurosci 2015(2):297672Google Scholar