Bipartite Synchronization Analysis of Fractional Order Coupled Neural Networks with Hybrid Control
- PDF / 555,274 Bytes
- 13 Pages / 439.37 x 666.142 pts Page_size
- 83 Downloads / 218 Views
Bipartite Synchronization Analysis of Fractional Order Coupled Neural Networks with Hybrid Control Lingzhong Zhang1
· Yongqing Yang2
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The bipartite synchronization problem for fractional order antagonistic coupled neural networks (FACNNs) is investigated in this paper. Using the properties of gamma function and special matrix, some criteria for bipartite Mittag–Leffler (M–L) synchronization and bipartite finite time synchronization of FACNNs have been obtained. To achieve bipartite finite time pinning synchronization, hybrid control strategy is designed. That is, finite time control combined with pinning control, pinning partial nodes, which can access the information of the leader. The upper bound of synchronization setting time is obtained. Keywords Hybrid control · Bipartite synchronization · Fractional order
1 Introduction Fractional calculus, at first look mysterious, is just one of misnomers which are the essence of mathematics. Fractional calculus is a name for the theory of calculus and derivations of arbitrary order [1]. Fractional differential equation, in describing the dynamic processes of heat conduction, gas diffusion in fractal porous media, has apparent advantages than integer one [2–4]. Since Leibniz and L’Hospital ˆ first proposed the definition of fractional derivative, fractional calculus and its application developed slowly. In 2008, fractional order neural network model was established and the dynamic behavior of fractional order neural network system was studied [5]. In recent years, more and more dynamic analysis of fractional order network systems has been studied and many excellent results have been produced [6–14].
This work was supported by the National Natural Science Foundation of China Nos. 61803049 and 61901062.
B
Yongqing Yang [email protected] Lingzhong Zhang [email protected]
1
School of Electrical Engineering and Automation, Changshu Institute of Technology, Changshu 215500, Jiangsu, PR China
2
School of IoT Engineering, Jiangnan University, Wuxi 214122, PR China
123
L. Zhang, Y. Yang
Most research works on the synchronization behavior are focused on coupled network with cooperative communication links of all nodes [15,16]. However, in practical application, there are competitive( antagonistic) communication links between adjacent nodes. In [17], the antagonism and cooperation among nodes are considered, the authors first introduced bipartite consensus concept, in which a group of nodes are synchronized to a manifold r (t) and the others are synchronized to −r (t), and it is proved that there is bipartite synchronization in the coupled network systems under the condition of structural balanced of signed graph. Recent years, much effort has been devoted to dynamic analysis of network systems with antagonistic communication links [18–21]. However, most of these works on bipartite synchronization of network systems focus on integer order systems. Until now, it is unclear how to s
Data Loading...
