Stochastic transition in a classical nonlinear dynamical system: A Lennard-Jones chain

1976 ◽  
Vol 29 (2) ◽  
pp. 1022-1027 ◽  
Author(s):  
E. Diana ◽  
L. Galgani ◽  
G. Casartelli ◽  
G. Casati ◽  
A. Scotti
Keyword(s):  
Dynamical System ◽  
Nonlinear Dynamical System ◽  
Nonlinear Dynamical ◽  
Lennard Jones ◽  
System A ◽  
Stochastic Transition

scholarly journals Multivaluedness in Networks: Exemplars

2020 ◽  
Author(s):  
Anton van Wyk ◽  
Guanrong Chen ◽  
Eric W. M. Wong
Keyword(s):  
Dynamical System ◽  
Random Process ◽  
Nonlinear Dynamical System ◽  
Linear Estimator ◽  
Nonlinear Dynamical ◽  
System A ◽  
Input And Output ◽  
Different Types ◽  
The Impact

This brief presents the first observations of multivaluedness in four systems: a random process, a nonlinear nondynamical system, a nonlinear dynamical system with nonlinearly sensed input and output and an adaptive linear estimator. The preliminary findings reported here, suggest the impact of multivaluedness in different types of networks to range from adverse to benign or even essential.

Multivaluedness in Networks: Exemplars

2020 ◽  
Author(s):  
Anton van Wyk ◽  
Guanrong Chen ◽  
Eric W. M. Wong
Keyword(s):  
Dynamical System ◽  
Random Process ◽  
Nonlinear Dynamical System ◽  
Linear Estimator ◽  
Nonlinear Dynamical ◽  
System A ◽  
Input And Output ◽  
Different Types ◽  
The Impact

This brief presents the first observations of multivaluedness in four systems: a random process, a nonlinear nondynamical system, a nonlinear dynamical system with nonlinearly sensed input and output and an adaptive linear estimator. The preliminary findings reported here suggest the impact of multivaluedness in different types of networks to range from adverse to benign or even essential.

scholarly journals Multivaluedness in Networks: Exemplars

2020 ◽  
Author(s):  
Anton van Wyk ◽  
Guanrong Chen ◽  
Eric W. M. Wong
Keyword(s):  
Dynamical System ◽  
Random Process ◽  
Nonlinear Dynamical System ◽  
Linear Estimator ◽  
Nonlinear Dynamical ◽  
System A ◽  
Input And Output ◽  
Different Types ◽  
The Impact

This brief presents the first observations of multivaluedness in four systems: a random process, a nonlinear nondynamical system, a nonlinear dynamical system with nonlinearly sensed input and output and an adaptive linear estimator. The preliminary findings reported here suggest the impact of multivaluedness in different types of networks to range from adverse to benign or even essential.

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

2008 ◽  
Vol 2008 ◽  
pp. 1-16 ◽  
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.

Prediction of Solutions of the Duffing System with Tuned Mass Damper

2020 ◽  
Vol 22 (4) ◽  
pp. 983-990
Author(s):  
Konrad Mnich
Keyword(s):  
Dynamical System ◽  
Duffing Oscillator ◽  
Probabilistic Approach ◽  
Nonlinear Dynamical System ◽  
Tuned Mass Damper ◽  
Nonlinear Dynamical ◽  
Duffing System ◽  
Mass Damper ◽  
Basin Stability ◽  
Stability Concept

AbstractIn this work we analyze the behavior of a nonlinear dynamical system using a probabilistic approach. We focus on the coexistence of solutions and we check how the changes in the parameters of excitation influence the dynamics of the system. For the demonstration we use the Duffing oscillator with the tuned mass absorber. We mention the numerous attractors present in such a system and describe how they were found with the method based on the basin stability concept.

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