Fixed-Time Synchronization of Complex-Valued Memristor-Based Neural Networks with Impulsive Effects
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Fixed-Time Synchronization of Complex-Valued Memristor-Based Neural Networks with Impulsive Effects Yanlin Zhang1 · Shengfu Deng1
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, the fixed-time synchronization of complex-valued memristor-based neural networks with impulsive effects is investigated. We first separate these complex-valued networks into real and imaginary parts, and design the appropriate controllers. Then apply the set-valued map and the differential inclusion theorem to handle the discontinuity problems at the righthand side of the drive-response systems. By constructing the comparison systems together with the Lyapunov function, we get the fixed-time synchronization conditions. Moreover, the estimate of the settling time is also explicitly obtained. Finally, two examples and their numerical simulations are presented to show the effectiveness of the obtained theoretical results. Keywords Fixed-time synchronization · Neural networks · Memristor-based · Impulsive · Complex-valued Mathematics Subject Classification 34D06 · 49N25 · 92B20 · 93C83
1 Introduction It is well known that the concept of the memristor (an abbreviation for the memory and the resistor) was first proposed by Chua [8] in 1971 which describes the relationship between the charge and the magnetic flux. It has been widely used lately, and is considered to be the fourth fundamental two-terminal circuit element besides the resistor, the capacitor and the inductor. Similar to the working principle of human brain synapses, the memristor has the function of memorizing the direction of the past charge flow. Because of this feature, its vast potential has been identified [10,17], and then it has become a hot topic due to its important roles in the next generation of computers and its powerful functions in human brain computers [20]. In the study of neural networks, the memristor instead of the resistor can be used to build a novel type of the neural network model called memristor-based neural network models (MNNs). Many meaningful studies [5,17,20,31,33,41,43] have been conducted.
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Shengfu Deng [email protected]; [email protected] School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
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Y. Zhang, S. Deng
Synchronization is an important dynamic behavior in neural networks and has already attracted extensive attention in the past few decades in various fields [2,4,5,24,27,47]. It has important applications in many areas such as information processing [36], chemical reaction [29] and secure communication [48]. A lot of synchronization types have been exploited theoretically and practically, for instance, complete synchronization [30], exponential synchronization [43], lag synchronization [20], adaptive synchronization [51], projective synchronization [38], phase synchronization [34], and pinning synchronization [23]. It is worth mentioning that the finite-time synchronization can be achieved in a desired finite time called settling time. If we consider the limited life
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