scholarly journals Chaos on Discrete Neural Network Loops with Self-Feedback

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Yuanlong Chen ◽  
Xiaoying Wu
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
Closed Set ◽  
Numerical Examples ◽  
Dynamical Behaviors ◽  
Symbolic Dynamical System ◽  
Theoretical Results

In this paper, the complex dynamical behaviors in a discrete neural network loop with self-feedback are studied. Specifically, an invariant closed set of the system of neural network loops is built and the subsystem restricted on this invariant closed set is topologically conjugate to a two-sided symbolic dynamical system which has two symbols. In the end, some illustrative numerical examples are given to demonstrate our theoretical results.

scholarly journals Dynamical Behaviors of Stochastic Reaction-Diffusion Cohen-Grossberg Neural Networks with Delays

2012 ◽  
Vol 2012 ◽  
pp. 1-14 ◽  
Author(s):  
Li Wan ◽  
Qinghua Zhou ◽  
Jizi Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Asymptotic Stability ◽  
Lyapunov Method ◽  
Reaction Diffusion ◽  
Ultimate Boundedness ◽  
Dynamical Behaviors ◽  
Weak Attractor ◽  
Stochastic Reaction ◽  
Theoretical Results

This paper investigates dynamical behaviors of stochastic Cohen-Grossberg neural network with delays and reaction diffusion. By employing Lyapunov method, Poincaré inequality and matrix technique, some sufficient criteria on ultimate boundedness, weak attractor, and asymptotic stability are obtained. Finally, a numerical example is given to illustrate the correctness and effectiveness of our theoretical results.

scholarly journals The Dynamical Analysis of Computer Viruses Model with Age Structure and Delay

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hui Cao ◽  
Si Wang ◽  
Dongxue Yan ◽  
Hongwu Tan ◽  
Hemiao Xu
Keyword(s):  
Age Structure ◽  
Reproduction Number ◽  
Dynamical Analysis ◽  
Acquired Immunity ◽  
Computer Viruses ◽  
Numerical Examples ◽  
Dynamical Behaviors ◽  
Stability And Instability ◽  
Theoretical Results ◽  
The Basic Reproduction Number

This paper deals with the dynamical behaviors for a computer viruses model with age structure, where the loss of the acquired immunity and delay are incorporated. Through some rigorous analyses, an explicit formula for the basic reproduction number of the model is calculated, and some results about stability and instability of equilibria for the model are established. These findings show that the age structure and delay can produce Hopf bifurcation for the computer viruses model. The numerical examples are executed to validate the theoretical results.

scholarly journals Adaptive Optimal Robust Control for Uncertain Nonlinear Systems Using Neural Network Approximation in Policy Iteration

2021 ◽  
Vol 11 (5) ◽  
pp. 2312
Author(s):  
Dengguo Xu ◽  
Qinglin Wang ◽  
Yuan Li
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Robust Control ◽  
Nonlinear Systems ◽  
Policy Iteration ◽  
Control Law ◽  
Globally Asymptotically Stable ◽  
Control Approach ◽  
Input Uncertainties ◽  
Theoretical Results

In this study, based on the policy iteration (PI) in reinforcement learning (RL), an optimal adaptive control approach is established to solve robust control problems of nonlinear systems with internal and input uncertainties. First, the robust control is converted into solving an optimal control containing a nominal or auxiliary system with a predefined performance index. It is demonstrated that the optimal control law enables the considered system globally asymptotically stable for all admissible uncertainties. Second, based on the Bellman optimality principle, the online PI algorithms are proposed to calculate robust controllers for the matched and the mismatched uncertain systems. The approximate structure of the robust control law is obtained by approximating the optimal cost function with neural network in PI algorithms. Finally, in order to illustrate the availability of the proposed algorithm and theoretical results, some numerical examples are provided.

A stable adaptive neural-network-based scheme for dynamical system control

2005 ◽  
Vol 285 (3) ◽  
pp. 653-667 ◽  
Author(s):  
X. Xu ◽  
Y.C. Liang ◽  
H.P. Lee ◽  
W.Z. Lin ◽  
S.P. Lim ◽  
...  
Keyword(s):  
Neural Network ◽  
Dynamical System ◽  
System Control ◽  
Adaptive Neural Network

scholarly journals A Novel Chaotic Neural Network Using Memristive Synapse with Applications in Associative Memory

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Xiaofang Hu ◽  
Shukai Duan ◽  
Lidan Wang
Keyword(s):  
Neural Network ◽  
Associative Memory ◽  
Large Scale ◽  
Cmos Technology ◽  
Chaotic Neural Network ◽  
Circuit Element ◽  
Nanoscale Cmos ◽  
Dynamical Behaviors ◽  
Implementation Scheme ◽  
Further Development

Chaotic Neural Network, also denoted by the acronym CNN, has rich dynamical behaviors that can be harnessed in promising engineering applications. However, due to its complex synapse learning rules and network structure, it is difficult to update its synaptic weights quickly and implement its large scale physical circuit. This paper addresses an implementation scheme of a novel CNN with memristive neural synapses that may provide a feasible solution for further development of CNN. Memristor, widely known as the fourth fundamental circuit element, was theoretically predicted by Chua in 1971 and has been developed in 2008 by the researchers in Hewlett-Packard Laboratory. Memristor based hybrid nanoscale CMOS technology is expected to revolutionize the digital and neuromorphic computation. The proposed memristive CNN has four significant features: (1) nanoscale memristors can simplify the synaptic circuit greatly and enable the synaptic weights update easily; (2) it can separate stored patterns from superimposed input; (3) it can deal with one-to-many associative memory; (4) it can deal with many-to-many associative memory. Simulation results are provided to illustrate the effectiveness of the proposed scheme.

scholarly journals Edge detection with trigonometric polynomial shearlets

2021 ◽  
Vol 47 (1) ◽  
Author(s):  
Kevin Schober ◽  
Jürgen Prestin ◽  
Serhii A. Stasyuk
Keyword(s):  
Edge Detection ◽  
Trigonometric Polynomial ◽  
Two Dimensions ◽  
Characteristic Functions ◽  
Numerical Examples ◽  
Special Cases ◽  
Periodic Characteristic ◽  
Boundary Curves ◽  
Theoretical Results ◽  
De La Vallée Poussin

AbstractIn this paper, we show that certain trigonometric polynomial shearlets which are special cases of directional de la Vallée Poussin-type wavelets are able to detect step discontinuities along boundary curves of periodic characteristic functions. Motivated by recent results for discrete shearlets in two dimensions, we provide lower and upper estimates for the magnitude of the corresponding inner products. In the proof, we use localization properties of trigonometric polynomial shearlets in the time and frequency domain and, among other things, bounds for certain Fresnel integrals. Moreover, we give numerical examples which underline the theoretical results.

scholarly journals Stability Analysis of Impulsive Control Systems with Finite and Infinite Delays

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Xuling Wang ◽  
Xiaodi Li ◽  
Gani Tr. Stamov
Keyword(s):  
Control Systems ◽  
Impulsive Control ◽  
Sufficient Conditions ◽  
Delay Systems ◽  
Stability Criteria ◽  
Numerical Examples ◽  
Infinite Delays ◽  
Impulsive Control Systems ◽  
Stable Matrix ◽  
Theoretical Results

This paper studies impulsive control systems with finite and infinite delays. Several stability criteria are established by employing the largest and smallest eigenvalue of matrix. Our sufficient conditions are less restrictive than the ones in the earlier literature. Moreover, it is shown that by using impulsive control, the delay systems can be stabilized even if it contains no stable matrix. Finally, some numerical examples are discussed to illustrate the theoretical results.

scholarly journals Nonlinear Dynamics and Chaos in Fractional-Order Hopfield Neural Networks with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Xia Huang ◽  
Zhen Wang ◽  
Yuxia Li
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Fractional Order ◽  
Hopfield Neural Network ◽  
Hopfield Neural Networks ◽  
Phase Portraits ◽  
Chaotic Attractors ◽  
Chaotic Motions ◽  
Dynamical Behaviors ◽  
Nonlinear Dynamics And Chaos

A fractional-order two-neuron Hopfield neural network with delay is proposed based on the classic well-known Hopfield neural networks, and further, the complex dynamical behaviors of such a network are investigated. A great variety of interesting dynamical phenomena, including single-periodic, multiple-periodic, and chaotic motions, are found to exist. The existence of chaotic attractors is verified by the bifurcation diagram and phase portraits as well.

Physical Essence of Stall Phenomena and its WNN-Based Aerodynamic Modeling from Flight Data

2014 ◽  
Vol 602-605 ◽  
pp. 3140-3143
Author(s):  
Xu Sheng Gan ◽  
Xue Qin Tang ◽  
Hai Long Gao
Keyword(s):  
Neural Network ◽  
Wavelet Neural Network ◽  
Flight Data ◽  
Numerical Examples ◽  
Aerodynamic Modeling ◽  
Aerodynamic Model ◽  
Aerodynamic Method ◽  
Physical Essence ◽  
Set Up

To understand the characteristics of aircraft stall for better aerodynamic model, the physical essence of the stall phenomena of aircraft is first introduced, and then a Wavelet Neural Network (WNN) is proposed to set up the stall aerodynamic model. Numerical examples indicates that through the deep cognition of the stall phenomena of aircraft the proposed stall aerodynamic method has a better accuracy than the traditional neural network and is also effective and feasible.

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