Exponential Synchronization of Complex-Valued Neural Networks Via Average Impulsive Interval Strategy
- PDF / 973,947 Bytes
- 18 Pages / 439.37 x 666.142 pts Page_size
- 8 Downloads / 200 Views
Exponential Synchronization of Complex-Valued Neural Networks Via Average Impulsive Interval Strategy Mei Liu1
· Zhanfeng Li1 · Haijun Jiang2 · Cheng Hu2 · Zhiyong Yu2
© Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract In this paper, the issue of the exponential synchronization for complex-valued neural networks with both discrete and distributed delays is investigated by applying impulsive control protocol. Based on the Lyapunov–Krasovskii function, average impulsive interval as well as the comparison principle, some simple verifiable sufficient criteria are established to guarantee the exponential synchronization between the master and the slave systems. Meanwhile, through the serious analysis of the networks systems, the exponential convergence rate can be specified. Additionally, a numerical example is finally given to illustrate the effectiveness of the proposed theoretical results. Keywords Exponential synchronization · Impulsive effects · Time-varying delay · Distributed delays
1 Introduction In the past few decades, there have been paid considerable attention in the dynamical behaviors of neural networks including bifurcation, stability, chaotic attractors and periodic attractors because of its wide applications in the area of secure communication, dynamic optimization, image processing, pattern recognition, associative memory [1]. At the same time, many different synchronization schemes have been well designed, such as complete synchronization [2], pinning synchronization [3], phase synchronization [4], projective synchronization [5], cluster synchronization [6], finite-time synchronization [7,8]. Among them, complete synchronization has captured a lot of researchers’ attention because of its applications in many areas, such as synchronous fireflies, swarming of fishes, flocking of birds. As a special kind of neural networks, complex-valued neural networks are the extension of real-valued neural networks. Compared with the real-valued neural networks, the state
B
Mei Liu [email protected]
1
School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, Henan, People’s Republic of China
2
College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, Xinjiang, People’s Republic of China
123
M. Liu et al.
vectors, connection weights and activation functions of the complex-valued neural networks are all complex values. In fact, complex-valued neural networks make it possible to solve some problems which cannot be solved by real-valued counterparts. For example, the XOR problem and the detection of symmetry problem [9] cannot be solved with their real-valued neuron, but they can be solved by a single complex-valued counterparts with the orthogonal decision boundaries [10]. Hence, it is very significant to investigate the dynamical behaviors of complex-valued neural networks, especially the synchronization of complex-valued neural networks. For example, in [11], adaptive complex hybrid projective synchronization of different dimensiona
Data Loading...
