Finite/Fixed-Time Bipartite Synchronization of Coupled Delayed Neural Networks Under a Unified Discontinuous Controller
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Finite/Fixed-Time Bipartite Synchronization of Coupled Delayed Neural Networks Under a Unified Discontinuous Controller Haocong Wu1 · Xia Wang1 · Xiaoyang Liu1 · Jinde Cao2
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract This paper considers the finite-time and fixed-time bipartite synchronization (FFTBS) of coupled delayed neural networks (CDNNs) under signed graphs. For the structurally balanced or unbalanced network topology, both the goals of FFTBS of CDNNs are achieved simultaneously by a unified discontinuous controller. Some sufficient criterion are obtained to ensure the FFTBS under the new designed protocols, and the corresponding settling times are estimated as well. Finally, two simulations are established to verify the validity and effectiveness of the designs. Keywords Bipartite synchronization · Discontinuous controllers · Finite time · Fixed time
1 Introduction In the past decades, there exists boosting interest in studying the dynamics of neural networks (NNs) due to their various potential applications in different fields, such as associative memory, pattern recognition and so on [1–3]. Recently, because the time delays are inevitable in many biological and artificial neural networks and will result in oscillation and instability, some theoretical and experimental attempts are greatly attached to the neural networks with constant or time-varying delays [4–6]. Especially, the synchronization issues of coupled delayed neural networks (CDNNs) have become a hot topic and received increasing
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Xia Wang [email protected] Haocong Wu [email protected] Xiaoyang Liu [email protected] Jinde Cao [email protected]
1
Research Center for Complex Networks and Swarm Intelligence, School of Computer Science and Technology, Jiangsu Normal University, Xuzhou 221116, China
2
School of Mathematics, Southeast University, Nanjing 210096, China
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H. Wu et al.
attention [7–9]. To name a few, Lu [10] investigated the synchronization issues of CDNNs by variational method. Yang [11] further studied synchronization problems of CDNNs with Markovian jumping and random coupling strength. Recently, there has been significant research effort devoted to the problems of finite-time synchronization because of its fast convergence rate and robust disturbance rejection ability [12–15]. Considering this, it is of great merits to ensure synchronization in a finite time. For instance, Du [16] solved finite-time leader-follower synchronization problems for secondorder nonlinear networks. Yang [17] addressed the finite-time synchronization issues of CDNNs with discontinuous activations and norm-bounded disturbances. However, it should be noticed that the settling time in many finite-time control is heavily dependent on the system initial values, which may be difficult to measure a priori for large systems. Regarding this, fixed-time synchronization issues are brought out, which means the settling time is independent of any initial values [18]. Later, Cao [19] discussed the fixed-time synchroni
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