scholarly journals Morphological Analysis for Three-Dimensional Chaotic Delay Neural Networks

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Yusong Lu ◽  
Ricai Luo ◽  
Yongfu Zou
Keyword(s):  
Neural Networks ◽  
Chaotic System ◽  
Morphological Analysis ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Hopfield Neural Network ◽  
Coefficient Matrix ◽  
Initial Value ◽  
The Neural Networks ◽  
And Control

The study focuses on the chaotic behavior of a three-dimensional Hopfield neural network with time delay. We find the aspecific coefficient matrix and the initial value condition of the system and use MATLAB software to draw its graph. The result shows that their shape is very similar to the figure of Roslerʼs chaotic system. Furthermore, we analyzed the divergence, the eigenvalue of the Jacobian matrix for the equilibrium point, and the Lyapunov exponent of the system. These properties prove that the system does have chaotic behavior. This result not only confirms that there is chaos in the neural networks but also that the chaotic characteristics of the system are very similar to those of Roslerʼs chaotic system under certain conditions. This discovery provides useful information that can be applied to other aspects of chaotic Hopfield neural networks, such as chaotic synchronization and control.

Neural Networks Based Attitude Decoupling Control for AUV with X-Shaped Fins

2013 ◽  
Vol 819 ◽  
pp. 222-228 ◽  
Author(s):  
Xiu Jun Sun ◽  
Jian Shi ◽  
Yan Yang
Keyword(s):  
Neural Networks ◽  
Attitude Control ◽  
Autonomous Underwater Vehicle ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Mathematic Model ◽  
On Line ◽  
The Neural Networks ◽  
Vehicle Motion ◽  
Three Dimensional Space

Attitude control in three-dimensional space for AUV (autonomous underwater vehicle) with x-shaped fins is complicated but advantageous. Yaw, pitch and roll angles of the vehicle are all associated with deflection angle of each fin while navigating underwater. In this paper, a spatial motion mathematic model of the vehicle is built by using theorem of momentum and angular momentum, and the hydrodynamic forces acting on x-shaped fins and three-blade propeller are investigated to clarify complex principle of the vehicle motion. In addition, the nonlinear dynamics equation which indicates the coupling relationship between attitude angles of vehicle and rotation angles of x-shaped fins is derived by detailed deduction. Moreover, a decoupling controller based on artificial neural networks is developed to address the coupling issue exposed in attitude control. The neural networks based controller periodically calculates and outputs deflection angles of fins according to the attitude angles measured with magnetic compass, thus the vehicles orientation can be maintained. By on-line training, twenty four weights in this controller converged according to index function.

scholarly journals A Three-Dimensional Infinite Collapse Map with Image Encryption

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1221
Author(s):  
Wenhao Yan ◽  
Zijing Jiang ◽  
Xin Huang ◽  
Qun Ding
Keyword(s):  
Image Encryption ◽  
Chaotic System ◽  
Chaotic Behavior ◽  
Security Analysis ◽  
Three Dimensional ◽  
Security Level ◽  
Encryption Scheme ◽  
Encryption Schemes ◽  
Low Dimensional ◽  
Differential Attacks

Chaos is considered as a natural candidate for encryption systems owing to its sensitivity to initial values and unpredictability of its orbit. However, some encryption schemes based on low-dimensional chaotic systems exhibit various security defects due to their relatively simple dynamic characteristics. In order to enhance the dynamic behaviors of chaotic maps, a novel 3D infinite collapse map (3D-ICM) is proposed, and the performance of the chaotic system is analyzed from three aspects: a phase diagram, the Lyapunov exponent, and Sample Entropy. The results show that the chaotic system has complex chaotic behavior and high complexity. Furthermore, an image encryption scheme based on 3D-ICM is presented, whose security analysis indicates that the proposed image encryption scheme can resist violent attacks, correlation analysis, and differential attacks, so it has a higher security level.

Nonfragile Fuzzy Output Feedback Synchronization of a New Chaotic System: Design and Implementation

2017 ◽  
Vol 13 (1) ◽  
Author(s):  
A. Azarang ◽  
M. Miri ◽  
S. Kamaei ◽  
M. H. Asemani
Keyword(s):  
Chaotic System ◽  
Output Feedback ◽  
Analog Circuit ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Nonlinear Controller ◽  
Full State ◽  
System Output ◽  
Takagi Sugeno ◽  
New System

A new three-dimensional (3D) chaotic system is proposed with four nonlinear terms which include two quadratic terms. To analyze the dynamical properties of the new system, mathematical tools such as Lyapunov exponents (LEs), Kaplan–York dimensions, observability constants, and bifurcation diagram have been exploited. The results of these calculations verify the specific features of the new system and further determine the effect of different system parameters on its dynamics. The proposed system has been experimentally implemented as an analog circuit which practically confirms its predicted chaotic behavior. Moreover, the problem of master–slave synchronization of the proposed chaotic system is considered. To solve this problem, we propose a new method for designing a nonfragile Takagi–Sugeno (T–S) fuzzy static output feedback synchronizing controller for a general chaotic T–S system and applied the method to the proposed system. Some practical advantages are achieved employing the new nonlinear controller as well as using system output data instead of the full-state data and considering gain variations because of the uncertainty in values of practical components used in implementation the controller. Then, the designed controller has been realized using analog devices to synchronize two circuits with the proposed chaotic dynamics. Experimental results show that the proposed nonfragile controller successfully synchronizes the chaotic circuits even with inexact analog devices.

scholarly journals A Numerical Method for Solving Fractional Differential Equations by Using Neural Network

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Haidong Qu ◽  
Xuan Liu
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Differential Equations ◽  
Fractional Differential Equations ◽  
Initial Value Problems ◽  
Numerical Solutions ◽  
Basis Functions ◽  
Initial Value ◽  
The Neural Networks ◽  
Fractional Differential

We present a new method for solving the fractional differential equations of initial value problems by using neural networks which are constructed from cosine basis functions with adjustable parameters. By training the neural networks repeatedly the numerical solutions for the fractional differential equations were obtained. Moreover, the technique is still applicable for the coupled differential equations of fractional order. The computer graphics and numerical solutions show that the proposed method is very effective.

Neural Network Pattern Recognition and its Application

2013 ◽  
Vol 756-759 ◽  
pp. 2438-2442 ◽  
Author(s):  
Hao Xu ◽  
Jin Gang Lai ◽  
Jiao Yu Liu ◽  
Neng Cao ◽  
Juan Zhao
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Pattern Recognition ◽  
System Identification ◽  
Nonlinear Function ◽  
Recognition System ◽  
The Neural Network ◽  
The Neural Networks ◽  
And Control ◽  
Network Pattern

many functions are possessed by the neural network such as parallel processing, self-learning and self-adapting. It could approximate any nonlinear function with any precision. A very effective way is provided by the neural network to deal with complex control problems, such as nonlinear, multivariable and uncertain ones etc. Therefore, the neural network is widely used in many aspects: pattern recognition, system identification and control fields and so on.It is developed in the paper about the application of neural networks pattern recognition and system identification. With MATLAB 6.1 and Visual Basic 6.0 design platform and developing tool, for some application instances, implement modeling, simulation and systematic test tasks of the neural networks pattern recognition and system identification. The above research and instances indicate that the neural networks pattern recognition and system identification based on MATLAB have better application prospects.

scholarly journals Lateral scanning logging while drilling data processing using convolutional neural networks

2022 ◽  
pp. 24-35
Author(s):  
K. N. Danilovskii ◽  
Loginov G. N.
Keyword(s):  
Neural Networks ◽  
Convolutional Neural Networks ◽  
Random Noise ◽  
Three Dimensional ◽  
Arbitrary Length ◽  
Drilling Data ◽  
The Neural Networks ◽  
Logging While Drilling ◽  
Geoelectric Layer ◽  
True Values

This article discusses a new approach to processing lateral scanning logging while drilling data based on a combination of three-dimensional numerical modeling and convolutional neural networks. We prepared dataset for training neural networks. Dataset contains realistic synthetic resistivity images and geoelectric layer boundary layouts, obtained based on true values of their spatial orientation parameters. Using convolutional neural networks two algorithms have been developed and programmatically implemented: suppression of random noise and detection of layer boundaries on the resistivity images. The developed algorithms allow fast and accurate processing of large amounts of data, while, due to the absence of full-connection layers in the neural networks’ architectures, it is possible to process resistivity images of arbitrary length.

scholarly journals Finite-time Stabilization for Uncertain Neural Networks With Time-varying Delay

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Neural Networks ◽  
Finite Time ◽  
Sufficient Conditions ◽  
Control Design ◽  
Time Varying ◽  
Time Varying Delay ◽  
The Neural Networks ◽  
Finite Time Boundedness ◽  
And Control ◽  
Varying Delay

In this paper, the problems of finite-time boundedness and control design for uncertain neuralnetworks with time-varying delay is considered. By constructing Lyapunov-Krasovskii function and using thematrix inequality method, sufficient conditions for finite-time boundedness of a class of neural networks withtime-varying delay are established. Then, we proposed a criterion to ensure that the neural networks with timevarying delay is finite-time stabilizable. A numerical example is given to verify the validity of the results.

WHAT CONNECTION TOPOLOGY PROHIBIT CHAOS IN CONTINUOUS TIME NETWORKS?

2007 ◽  
Vol 10 (04) ◽  
pp. 449-461 ◽  
Author(s):  
XIAO-SONG YANG ◽  
QUAN YUAN ◽  
LIN WANG
Keyword(s):  
Neural Network ◽  
Neural Networks ◽  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Continuous Time ◽  
Chaotic Behavior ◽  
Three Dimensional ◽  
Direct Connection ◽  
The Third

In this paper, we are concerned with two interesting problems in the dynamics of neural networks. What connection topology will prohibit chaotic behavior in a continuous time neural network (NN). To what extent is a continuous time neural network (NN) described by continuous ordinary differential equations simple enough yet still able to exhibit chaos? We study these problems in the context of the classical neural networks with three neurons, which can be described by three-dimensional autonomous ordinary differential equations. We first consider the case where there is no direct interconnection between the first neuron and the third neuron. We then discuss the case where each pair of neurons has a direct connection. We show that the existence of the directed loop in connection topology is necessary for chaos to occur.

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