scholarly journals Preface: Modelling and numerical simulations of dynamical systems

2017 ◽  
Vol 87 (5) ◽  
pp. 783-784
Author(s):  
Jan Awrejcewicz ◽  
Nuno Maia ◽  
Jerzy Mrozowski
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations

The Stick Motion of a Harmonically Excited, Friction-Induced Oscillator on a Sinusoidally Traveling Surface

2006 ◽  
Author(s):  
Albert C. J. Luo ◽  
Brandon C. Gegg ◽  
Steve S. Suh
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Dry Friction ◽  
The Other ◽  
Linear Oscillator ◽  
Analytical Prediction ◽  
Nonlinear Friction ◽  
Friction Forces

In this paper, the methodology is presented through investigation of a periodically, forced linear oscillator with dry friction, resting on a traveling surface varying with time. The switching conditions for stick motions in non-smooth dynamical systems are obtained. From defined generic mappings, the corresponding criteria for the stick motions are presented through the force product conditions. The analytical prediction of the onset and vanishing of the stick motions is illustrated. Finally, numerical simulations of stick motions are carried out to verify the analytical prediction. The achieved force criteria can be applied to the other dynamical systems with nonlinear friction forces possessing a CO - discontinuity.

scholarly journals Application of Piecewise Successive Linearization Method for the Solutions of the Chen Chaotic System

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
S. S. Motsa ◽  
Y. Khan ◽  
S. Shateyi
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Chaotic System ◽  
Good Accuracy ◽  
Linearization Method ◽  
Chen System ◽  
Successive Linearization Method ◽  
Runge Kutta

This paper centres on the application of the new piecewise successive linearization method (PSLM) in solving the chaotic and nonchaotic Chen system. Numerical simulations are presented graphically and comparison is made between the PSLM and Runge-Kutta-based methods. The work shows that the proposed method provides good accuracy and can be easily extended to other dynamical systems including those that are chaotic in nature.

Periodic Motions in an Autonomous System With a Discontinuous Vector Field

2020 ◽  
Author(s):  
Siyu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Vector Field ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Autonomous System ◽  
Parameter Study ◽  
Spring Stiffness ◽  
Algebraic Equations ◽  
Periodic Motions ◽  
Mapping Structures ◽  
The Stability

Abstract In this paper, periodic motions in an autonomous system with a discontinuous vector field are discussed. The periodic motions are obtained by constructing a set of algebraic equations based on motion mapping structures. The stability of periodic motions is investigated through eigenvalue analysis. The grazing bifurcations are presented by varying the spring stiffness. Once the grazing bifurcation occurs, periodic motions switches from the old motion to a new one. Numerical simulations are conducted for motion illustrations. The parameter study helps one understand autonomous discontinuous dynamical systems.

scholarly journals Some Problems of Feedback Control Strategies and It’s Treatment

2017 ◽  
Vol 9 (1) ◽  
pp. 39 ◽  
Author(s):  
Maysoon M. Aziz ◽  
Saad Fawzi AL-Azzawi
Keyword(s):  
Dynamical Systems ◽  
Feedback Control ◽  
Numerical Simulations ◽  
Positive Feedback ◽  
Control Strategies ◽  
Novel Approach

This paper extends and improves the feedback control strategies. In detailed, the ordinary feedback, dislocated feedback, speed feedback and enhancing feedback control for a several dynamical systems are discussed here. It is noticed that there some problems by these strategies. For this reason, this Letter proposes a novel approach for treating these problems. The results obtained in this paper show that the strategies with positive feedback coefficients can be controlled in two cases and failed in another two cases. Theoretical and numerical simulations are given to illustrate and verify the results.

STRANGE ATTRACTORS IN PERIODICALLY KICKED CHUA'S CIRCUIT

2005 ◽  
Vol 15 (01) ◽  
pp. 83-98 ◽  
Author(s):  
QIUDONG WANG ◽  
ALI OKSASOGLU
Keyword(s):  
Hopf Bifurcation ◽  
Dynamical Systems ◽  
Numerical Simulations ◽  
Autonomous System ◽  
Strange Attractors ◽  
External Forcing ◽  
Chua’S Circuit ◽  
New Developments ◽  
Chua's Circuit

In this paper, we discuss a new mechanism for chaos in light of some new developments in the theory of dynamical systems. It was shown in [Wang & Young, 2002b] that strange attractors occur when an autonomous system undergoing a generic Hopf bifurcation is subjected to a weak external forcing that is periodically turned on and off. For illustration purposes, we apply these results to the Chua's system. Derivation of conditions for chaos along with the results of numerical simulations are presented.

scholarly journals Generalized Projective Synchronization for Different Hyperchaotic Dynamical Systems

2011 ◽  
Vol 2011 ◽  
pp. 1-19 ◽  
Author(s):  
M. M. El-Dessoky ◽  
E. Saleh
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Lorenz System ◽  
Sufficient Conditions ◽  
Projective Synchronization ◽  
Hyperchaotic Lorenz System ◽  
Generalized Projective Synchronization ◽  
Hyperchaotic Systems

Projective synchronization and generalized projective synchronization have recently been observed in the coupled hyperchaotic systems. In this paper a generalized projective synchronization technique is applied in the hyperchaotic Lorenz system and the hyperchaotic Lü. The sufficient conditions for achieving projective synchronization of two different hyperchaotic systems are derived. Numerical simulations are used to verify the effectiveness of the proposed synchronization techniques.

Analytical Dynamics of a Ball Bouncing on a Vibrating Table

2012 ◽  
Author(s):  
Yu Guo ◽  
Albert C. J. Luo
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Analytical Dynamics ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Theory Of Flow ◽  
Mapping Structures ◽  
Ball Bouncing ◽  
Vibrating Table

In this paper, the theory of flow switchability for discontinuous dynamical systems is applied. Domains and boundaries for such a discontinuous problem are defined and analytical conditions for motion switching are developed. The conditions explain the important role of switching phase on the motion switchability in such a system. To describe different motions, the generic mappings and mapping structures are introduced. Bifurcation scenarios for periodic and chaotic motions are presented for different motions and switchability. Numerical simulations are provided for periodic motions with impacts only and with impact chatter to stick in the system.

scholarly journals Generalized synchronization of identical and nonidentical chaotic dynamical systems via master approaches

2017 ◽  
Vol 7 (3) ◽  
pp. 248-254
Author(s):  
Shko Ali-Tahir ◽  
Murat Sari ◽  
Abderrahman Bouhamidi
Keyword(s):  
Dynamical Systems ◽  
Numerical Simulations ◽  
Lyapunov Stability ◽  
Stability Theory ◽  
Lyapunov Stability Theory ◽  
Generalized Synchronization ◽  
Chaotic Dynamical Systems

The main objective of this work is to discuss a generalized synchronization of a coupled chaotic identicaland nonidentical dynamical systems. We propose a method used to study generalized synchronization in masterslavesystems. This method, is based on the classical Lyapunov stability theory, utilizes the master continuous timechaotic system to monitor the synchronized motions. Various numerical simulations are performed to verify theeffectiveness of the proposed approach.

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