Synchronization control for memristive high-order competitive neural networks with time-varying delay☆
Introduction
In recent decades, neural networks have been widely applied in many areas because of their associative memory function and adaptive capacity. However, many scholars mainly focus on the study of neural networks with only one type of state variable, such as some classical neural networks including Hopfield neural network, BAM neural network and BP neural network. Actually, there also exist some neural networks with more than one type of state variable, such as competitive neural network which was put forward by Cohen and Grossberg [1] in 1983. About thirteen years later, Meyer-Bäse first proposed a competitive neural network model with different time scales [2], which has two different types of state variables, i.e., short-term memory and long-term memory. Moreover, he pointed out that short-term memory describes the fast neural activity level and long-term memory describes the slow unsupervised synaptic modifications. Some self-organizing networks can be constructed from competitive neural network because it is usually unsupervised learning, such as self-organizing map networks, counterpropagation networks.
Synchronization has attracted considerable attention of researchers due to its wide potential applications, such as secure communication [3], [4], [5], chemical reactions [6] and information science [7]. Recently, the related results on synchronization of competitive neural networks with different types of time delays have been obtained [8], [9], [10], [11]. In [8], the author designed an adaptive feedback controller to ensure that competitive neural networks with stochastic perturbation are synchronized. In [9], the authors studied synchronization problem of the competitive neural network model with mixed delays subjected to unknown hybrid perturbations. In [10], the LMI approach was adopted to achieve global exponential synchronization for the switched competitive neural networks with mixed delays subjected to stochastic disturbance by designing a delay-dependent controller. In [11], an adaptive controller was employed to ensure that delayed competitive neural networks are globally synchronized.
Compared with traditional neural networks, neural networks with high-order terms, called high-order neural networks, have better performances [12], [13], [14], such as greater storage capacity, faster convergence rate, higher fault tolerance and stronger approximation property. Obviously, it is necessary to investigate the synchronization of high-order neural networks. However, there exist few results about the synchronization of high-order neural networks [12]. In [12], some sufficient conditions of global exponential synchronization for second-order recurrent neural networks with mixed delays were derived. In [15], the high-order term is introduced into competitive neural network to built a new model, which is called high-order competitive neural networks.
In the circuit implementation for neural networks, we generally use resistors to simulate synapse among the neurons [16]. We know that the synapse plays a key role in the formation of memory, but the resistor has no memory function. Due to the complexity of the human brain, in order to better describe the human brain, we should replace resistor with memristor, which was first put forward by Chua [17] in 1971. Unfortunately, the memristor failed to attract much attention, until 2008 when the researchers of Hewlett-Packard laboratory built the first memristor device [18]. Since the memristor has the memory function, memristive neural networks can better simulate the human brain [19], [20], [21], [22], [23], [24]. As far as we know, almost no results on the synchronization problem of memristive high-order competitive neural networks have been obtained. Then, we cannot help asking how to solve this problem.
Based on the above discussion, the object of this paper is to study the synchronization problem of memristive high-order competitive neural network with time delay. Some novel criteria for global exponential synchronization of MHCNNs are obtained by utilizing Lyapunov function method, which can be divided into algebraic form and matrix form. Moreover, the existence of Fillipov solution of the drive system and the response system is also proved by using differential inclusion theory.
The structure of this paper is organized as follows. The model of delayed MHCNN is formulated and some preliminaries are presented in Section 2. In Section 3, the sufficient conditions for global exponential synchronization of the drive-response system are derived. In Section 4, two examples and numerical simulations are given to substantiate the effectiveness of our results. Finally, the conclusions are drawn in Section 5.
Section snippets
Preliminaries
First, the following memristive high-order competitive neural network (MHCNN) with time-varying delay is considered:where xi(t) is the neuron state, ai > 0 represents the decay of the neuron, bi is the strength of the external stimulus, ci > 0
Main results
By using Lyapunov method, the following criteria for global exponential synchronization of systems (2) and (6) are presented in this section. Theorem 1 Assume that Assumptions 1 and 2 hold. Then response MHCNN (6) can be globally exponentially synchronized with drive MHCNN (2) at the rate δ under controller (8), if there exist positive numbers pi and qi, such thatand
Numerical simulation
Consider the two-neuron delayed memrisive high-order competitive neural networkwhere the activation function satisfies the Assumption 1 with and . LetIn addition, the matrices
Conclusion
The synchronization problem of memristive high-order competitive neural network with time-varying delay has been discussed. By utilizing Lyapunov method and some inequality techniques, several criteria have been obtained to realize the global exponential synchronization between drive system and response system.
Time-triggered control, event-triggered control, pinning control and impulsive control are becoming more and more popular because of the limitation of storage resources. The further work
Declarations of interest
None.
Shuqing Gong received his B.S. degree from Anyang Normal University, Anying, China in 2013, and was admitted to College of Mathematics and Econometrics, Hunan University, Changsha, China in 2014. His research interests include neural networks, switched systems, memristive systems and networked control systems.
References (41)
Adaptive synchronization for competitive neural networks with different time scales and stochastic perturbation
Neurocomputing
(2009)- et al.
Matrix measure based stability criteria for high-order neural networks with proportional delay
Neurocomputing
(2015) - et al.
Periodic attractor for reaction-diffusion high-order Hopfield neural networks with time-varying delays
Comput. Math. Appl.
(2017) - et al.
Multistability and multiperiodicity of high-order competitive neural networks with a general class of activation functions
Neurocomputing
(2012) - et al.
Synchronization control of memristor-based recurrent neural networks with perturbations
Neural Netw.
(2014) - et al.
Matrix measure strategies for stability and synchronization of inertial BAM neural network with time delays
Neural Netw.
(2014) - et al.
Global exponential dissipativity and stabilization of memristor-based recurrent neural networks with time-varying delays
Neural Netw.
(2013) - et al.
Periodicity and dissipativity for memristor-based mixed time-varying delayed neural networks via differential inclusions
Neural Netw.
(2014) - et al.
Finite-time synchronization of inertial memristive neural networks with time delay via delay-dependent control
Neurocomputing
(2018) - et al.
Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays
Neurocomputing
(2006)
Robust control of a class of uncertain nonlinear systems
Syst. Control Lett.
Absolute exponential stability of recurrent neural networks with Lipschitz-continuous activation functions and time delays
Neural Netw.
Adaptive synchronization of neural networks with time-varying delay and distributed delay
Phys. A Stat. Mech. Appl.
Synchronization of memristor-based recurrent neural networks with two delay components based on second-order reciprocally convex approach
Neural Netw.
Absolute stability of global pattern formation and parallel memory storage by competitive neural networks
IEEE Trans. Syst. Man Cybern.
Singular perturbation analysis of competitive neural networks with different time-scales
Neural Comput.
Coupled nonlinear oscillators and the symmetries of animal gaits
J. Nonlinear Sci.
Co-occurrence of northern and southern hemisphere blocks as partially synchronized chaos
J. Atmos. Sci.
An observer-based approach for chaotic synchronization with applications to secure communications
IEEE Trans. Circuits Syst. I Fundam. Theory Appl.
Robust adaptive neural network synchronization controller design for a class of time delay uncertain chaotic systems
Chaos Solitons Fractals
Cited by (7)
Finite-time synchronization of T-S fuzzy memristive neural networks with time delay
2023, Fuzzy Sets and SystemsCitation Excerpt :As the fourth basic element in circuit, memristor has attracted much attention since it was proposed. Particularly, as a good substitute for resistance, it is applied to neural networks, and then produces memristive neural network [8–14]. A question is naturally raised: what is the performance of fuzzy memristive neural networks which are composed of fuzzy logic and memristive neural networks?
Global exponential synchronization of discrete-time high-order switched neural networks and its application to multi-channel audio encryption
2023, Nonlinear Analysis: Hybrid SystemsCitation Excerpt :As mentioned above, the synchronization control problem of neural networks has shown very good application value in audio encryption [25,26], image encryption [27] and other fields, so it has attracted the attention of many scholars. For example, the complete synchronization control problem of discrete-time switched delayed NNs is investigated by employing the average dwell time method in [28]; the lag synchronization control problem of continuous-time inertial delayed NNs is solved by using inequality techniques in [29]; and the complete synchronization control problem of continuous-time memristive high-order competitive delayed NNs is researched by employing some inequality techniques in [30]. Unfortunately, the synchronization control problem of DHONNs has not been studied (whether complete synchronization or lag synchronization).
Exponential Synchronization of Memristor-Based Competitive Neural Networks With Reaction- Diffusions and Infinite Distributed Delays
2024, IEEE Transactions on Neural Networks and Learning SystemsFixed-time synchronization of complex-valued memristive competitive neural networks based on two novel fixed-time stability theorems
2023, Neural Computing and Applications
Shuqing Gong received his B.S. degree from Anyang Normal University, Anying, China in 2013, and was admitted to College of Mathematics and Econometrics, Hunan University, Changsha, China in 2014. His research interests include neural networks, switched systems, memristive systems and networked control systems.
Zhenyuan Guo received the B.S. degree in mathematics and applied mathematics and the Ph.D. degree in applied mathematics from the College of Mathematics and Econometrics, Hunan University, Changsha, China, in 2004 and 2009, respectively. He was a joint Ph.D. student with the Department of Applied Mathematics, University of Western Ontario, London, ON, Canada, from 2008 to 2009. He was a Post-Doctoral Research Fellow with the Department of Mechanical and Automation Engineering, Chinese University of Hong Kong, Hong Kong, from 2013 to 2015. He is currently the Professor with the College of Mathematics and Econometrics, Hunan University. His current research interests include the theory of functional differential equations and differential equations with discontinuous right hands, and their applications to the dynamics of neural networks, memristive systems, and control systems.
Shiping Wen received the M.Eng. degree in control science and engineering from the School of Automation, Wuhan University of Technology, Wuhan, China, in 2010, and the Ph.D degree in control science and engineering from the School of Automation, Huazhong University of Science and Technology, Wuhan, in 2013. He is currently an Associate Professor at School of Automation, Huazhong University of Science and Technology, and also in the Key Laboratory of Image Processing and Intelligent Control of Education Ministry of China, Wuhan, China. His current research interests include memristor-based circuits and systems, neural networks, and deep learning.
Tingwen Huang received the B.S. degree in mathematics from Southwest Normal University (currently, Southwest University), Chongqing, China, in 1990, the M.S. degree in mathematics from Sichuan University, Chengdu, China, in 1993, and the Ph.D. degree in mathematics from Texas A&M University, College Station, TX, USA, in 2002. He was a Visiting Assistant Professor with Texas A&M University. Then, he joined Texas A&M University at Qatar, Doha, Qatar, as an Assistant Professor in 2003, where he was promoted to a Professor in 2013. He has published over 300 peer-review reputable journal papers, including over 100 papers in IEEE TRANSACTIONS. His current research interests include neural-networks-based computational intelligence, distributed control and optimization, and nonlinear dynamics and applications in smart grids. Prof.Huang serves as an Associate Editor for four journals, including the IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS, the IEEE TRANSACTIONS ON CYBERNETICS, and Cognitive Computation.
- ☆
Research supported by National Natural Science Foundation of China (61573003), Natural Science Foundation of Hunan (2019JJ40022) and NPRP grants: NPRP 9-466-1-103 from Qatar National Research Fund.