A time delay neural network for dynamical system control

Author(s):  
X. Xu ◽  
L.M. Wan ◽  
X.L. Wang ◽  
L.K. Wang ◽  
Y.C. Liang
2005 ◽  
Vol 285 (3) ◽  
pp. 653-667 ◽  
Author(s):  
X. Xu ◽  
Y.C. Liang ◽  
H.P. Lee ◽  
W.Z. Lin ◽  
S.P. Lim ◽  
...  

Author(s):  
Daniela Danciu

Neural networks—both natural and artificial, are characterized by two kinds of dynamics. The first one is concerned with what we would call “learning dynamics”. The second one is the intrinsic dynamics of the neural network viewed as a dynamical system after the weights have been established via learning. The chapter deals with the second kind of dynamics. More precisely, since the emergent computational capabilities of a recurrent neural network can be achieved provided it has suitable dynamical properties when viewed as a system with several equilibria, the chapter deals with those qualitative properties connected to the achievement of such dynamical properties as global asymptotics and gradient-like behavior. In the case of the neural networks with delays, these aspects are reformulated in accordance with the state of the art of the theory of time delay dynamical systems.


Author(s):  
Rozaida Ghazali ◽  
Abir Hussain ◽  
Nazri Mohd Nawi

This chapter proposes a novel Dynamic Ridge Polynomial Higher Order Neural Network (DRPHONN). The architecture of the new DRPHONN incorporates recurrent links into the structure of the ordinary Ridge Polynomial Higher Order Neural Network (RPHONN) (Shin & Ghosh, 1995). RPHONN is a type of feedforward Higher Order Neural Network (HONN) (Giles & Maxwell, 1987) which implements a static mapping of the input vectors. In order to model dynamical functions of the brain, it is essential to utilize a system that is capable of storing internal states and can implement complex dynamic system. Neural networks with recurrent connections are dynamical systems with temporal state representations. The dynamic structure approach has been successfully used for solving varieties of problems, such as time series forecasting (Zhang & Chan, 2000; Steil, 2006), approximating a dynamical system (Kimura & Nakano, 2000), forecasting a stream flow (Chang et al, 2004), and system control (Reyes et al, 2000). Motivated by the ability of recurrent dynamic systems in real world applications, the proposed DRPHONN architecture is presented in this chapter.


2019 ◽  
Author(s):  
Ye Bai ◽  
Jiangyan Yi ◽  
Jianhua Tao ◽  
Zhengqi Wen ◽  
Zhengkun Tian ◽  
...  

2020 ◽  
Vol 28 (2) ◽  
pp. 243-250 ◽  
Author(s):  
Yu Chen ◽  
Jin Cheng ◽  
Yu Jiang ◽  
Keji Liu

AbstractIn this paper, we propose a novel dynamical system with time delay to describe the outbreak of 2019-nCoV in China. One typical feature of this epidemic is that it can spread in the latent period, which can therefore be described by time delay process in the differential equations. The accumulated numbers of classified populations are employed as variables, which is consistent with the official data and facilitates the parameter identification. The numerical methods for the prediction of the outbreak of 2019-nCoV and parameter identification are provided, and the numerical results show that the novel dynamic system can well predict the outbreak trend so far. Based on the numerical simulations, we suggest that the transmission of individuals should be greatly controlled with high isolation rate by the government.


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