BIFURCATION IN A NONLINEAR DYNAMICAL SYSTEM ARISING FROM SEEKING STEADY STATES OF A NEURAL NETWORK

We show that in an artificial dynamic neural network that depends on a real parameter μ, steady states do not exist for μ ≤ -2, and positive and negative steady states exist for μ > -2. We hope that such a bifurcation phenomenon in our network model may explain some of the real observations in nature.

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Adaptive high-order Hopfield-based neural network tracking controller for uncertain nonlinear dynamical system

2010 International Conference on Networking, Sensing and Control (ICNSC) ◽

10.1109/icnsc.2010.5461534 ◽

2010 ◽

Author(s):

Chi-Hsu Wang ◽

Kun-Neng Hung

Keyword(s):

Neural Network ◽

Dynamical System ◽

Nonlinear Dynamical System ◽

High Order ◽

Nonlinear Dynamical ◽

Tracking Controller

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Feedforward neural network based nonlinear dynamical system function reconstruction

ICECS'99. Proceedings of ICECS '99. 6th IEEE International Conference on Electronics, Circuits and Systems (Cat. No.99EX357) ◽

10.1109/icecs.1999.812277 ◽

2003 ◽

Author(s):

He Jianhua ◽

Yong Zongkai ◽

Wang Shu ◽

Chen Wenqing

Keyword(s):

Neural Network ◽

Dynamical System ◽

Nonlinear Dynamical System ◽

Feedforward Neural Network ◽

System Function ◽

Nonlinear Dynamical ◽

Function Reconstruction

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ON THE MATHEMATICAL CLARIFICATION OF THE SNAP-BACK-REPELLER IN HIGH-DIMENSIONAL SYSTEMS AND CHAOS IN A DISCRETE NEURAL NETWORK MODEL

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127402004966 ◽

2002 ◽

Vol 12 (05) ◽

pp. 1129-1139 ◽

Cited By ~ 26

Author(s):

WEI LIN ◽

JIONG RUAN ◽

WEIRUI ZHAO

Keyword(s):

Neural Network ◽

Dynamical System ◽

Neural Networks ◽

Fixed Point ◽

Numerical Simulations ◽

Neural Network Model ◽

Jacobian Matrix ◽

Nonlinear Dynamical System ◽

High Dimensional ◽

Nonlinear Dynamical

We investigate the differences among several definitions of the snap-back-repeller, which is always regarded as an inducement to produce chaos in nonlinear dynamical system. By analyzing the norms in different senses and the illustrative examples, we clarify why a snap-back-repeller in the neighborhood of the fixed point, where all eigenvalues of the corresponding variable Jacobian Matrix are absolutely larger than 1 in norm, might not imply chaos. Furthermore, we theoretically prove the existence of chaos in a discrete neural networks model in the sense of Marotto with some parameters of the systems entering some regions. And the following numerical simulations and corresponding calculation, as concrete examples, reinforce our theoretical proof.

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On Approximate Treatment of Nonlinear Dynamical System of an Electrostatically Actuated Micro-Cantilever

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.29-32.2211 ◽

2010 ◽

Vol 29-32 ◽

pp. 2211-2218 ◽

Cited By ~ 1

Author(s):

Y.M. Chen ◽

Guang Meng ◽

J.K. Liu

Keyword(s):

Dynamical System ◽

Taylor Series ◽

Nonlinear Dynamical System ◽

Real System ◽

Nonlinear Dynamical ◽

The Real ◽

Electrostatically Actuated ◽

Micro Cantilever ◽

Approximate Treatment

This paper analyzed an approximate treatment of the nonlinear dynamical system of an electrostatically actuated micro-cantilever subjected to combined parametric and forcing excitations in MEMS. In this approximation, the nonlinearity is expanded into Taylor series. By retaining a number of terms, a modified system is obtained and then employed to study the real system indirectly. Bifurcations and sub-harmonic responses of the real system and of the modified system are obtained via numerical integrating methods. It was found, modified systems with only several terms cannot simulate multi-periodic and quasi-periodic responses of the real system. However, as long as enough terms are taken into account, the modified systems can give rise up the real responses no matter how complex they are.

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Extended and unscented kalman filters for artificial neural network modelling of a nonlinear dynamical system

Theoretical Foundations of Chemical Engineering ◽

10.1134/s0040579512030074 ◽

2012 ◽

Vol 46 (3) ◽

pp. 274-278 ◽

Cited By ~ 6

Author(s):

A. Saptoro

Keyword(s):

Neural Network ◽

Dynamical System ◽

Artificial Neural Network ◽

Kalman Filters ◽

Nonlinear Dynamical System ◽

Network Modelling ◽

Nonlinear Dynamical ◽

Neural Network Modelling ◽

Artificial Neural ◽

Artificial Neural Network Modelling

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Recognition of stability domain of nonlinear dynamical system using multilayer feed-forward artificial neural network approach

[1991 Proceedings] The Twenty-Third Southeastern Symposium on System Theory ◽

10.1109/ssst.1991.138550 ◽

2002 ◽

Cited By ~ 3

Author(s):

D.R. Marpaka

Keyword(s):

Neural Network ◽

Dynamical System ◽

Artificial Neural Network ◽

Nonlinear Dynamical System ◽

Stability Domain ◽

Network Approach ◽

Neural Network Approach ◽

Feed Forward ◽

Nonlinear Dynamical ◽

Artificial Neural Network Approach

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Identification of Stochastic Loads Applied to a Nonlinear Dynamical System Using an Uncertain Computational Model

Mathematical Problems in Engineering ◽

10.1155/2008/181548 ◽

2008 ◽

Vol 2008 ◽

pp. 1-16 ◽

Cited By ~ 1

Author(s):

C. Soize ◽

A. Batou

Keyword(s):

Dynamical System ◽

Computational Model ◽

Nonlinear Dynamical System ◽

Likelihood Method ◽

Parameter Uncertainties ◽

Model Uncertainties ◽

Nonlinear Dynamical ◽

The Real ◽

System A ◽

Stochastic Loads

This paper deals with the identification of stochastic loads applied to a nonlinear dynamical system for which a few experimental responses are available using an uncertain computational model. Uncertainties are induced by the use of a simplified computational model to predict the responses of the real system. A nonparametric probabilistic approach of both parameter uncertainties and model uncertainties is implemented in the simplified computational model in order to take into account uncertainties. The level of uncertainties is identified using the maximum likelihood method. The identified stochastic simplified computational model which is obtained is then used to perform the identification of the stochastic loads applied to the real nonlinear dynamical system. A numerical validation of the complete methodology is presented.

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