Periodic Solution and Strange Attractor in Impulsive Hopfield Networks with Time-Varying Delays
By constructing suitable Lyapunov functions, we study the existence, uniqueness and global exponential stability of periodic solution for impulsive Hopfield neural networks with time-varying delays. Our condition extends and generalizes a known condition
- PDF / 598,370 Bytes
- 14 Pages / 439.37 x 666.142 pts Page_size
- 3 Downloads / 149 Views
Abstract By constructing suitable Lyapunov functions, we study the existence, uniqueness and global exponential stability of periodic solution for impulsive Hopfield neural networks with time-varying delays. Our condition extends and generalizes a known condition for the global exponential periodicity of continuous Hopfield neural networks with time-varying delays. Further the numerical simulation shows that our system can occur many forms of complexities including gui strange attractor and periodic solution. Keywords Hopfield neural network · Lyapunov functions · Pulse · Time-varying delay · Periodic solution · Strange attractor
1 Introduction In recent years, stability of different classes of neural networks with time delay, such as Hopfield neural networks, cellular neural networks, bidirectional associative neural networks, Lotka-Volterra neural networks, has been extensively studied and various stability conditions have been obtained for these models of neural Y. Cheng (B) The School of Science, Beijing Forestry University, Beijing 100083, People’s Republic of China e-mail: [email protected] Y. Yan The School of Mathematics and Statistics, Hainan Normal University, Haikou, Hainan 571158, People’s Republic of China e-mail: [email protected] Z. Gui Department of Software Engineering, Hainan College of Software Technology, QiongHai, Hainan 571400, People’s Republic of China e-mail: [email protected] G-C. Yang et al.(eds.), IAENG Transactions on Engineering Technologies, Lecture Notes in Electrical Engineering 229, DOI: 10.1007/978-94-007-6190-2_2, © Springer Science+Business Media Dordrecht 2013
17
18
Y. Cheng et al.
networks. A citation will look like this, [1, 3, 6]. Here are some more citations [5, 10, 13, 16, 17]. Stability and convergence properties are generally regarded as important effects of delays. Both in biological and man-made neural systems, integration and communication delays are ubiquitous, and often become sources of instability. The delays in electronic neural networks are usually time varying, and sometimes vary violently with time due to the finite switching speed of amplifiers and faults in the electrical circuit. They slow down the transmission rate and tend to introduce some degree of instability in circuits. Therefore, fast response must be required in practical electronic neural-network designs. The technique to achieve fast response troubles many circuit designers. So, it is important to investigate the delay independent stability and decay estimates of the states of analog neural networks. However, in implementation of networks, time delays are inevitably encountered because of the finite switching speed of amplifiers, see [2, 4, 7, 11, 12]. On the other hand, impulsive effect likewise exists in a wide variety of evolutionary processes in which states are changed abruptly at certain moments of time, involving such fields as medicine and biology, economics, mechanics, electronics and telecommunications, etc. Many interesting results on impulsive effect have been gained. Here a
Data Loading...
