On the dynamics of a simplified canonical Chua’s oscillator with smooth hyperbolic sine nonlinearity: Hyperchaos, multistability and multistability control

2019 ◽  
Vol 29 (11) ◽  
pp. 113105 ◽  
Author(s):  
T. Fonzin Fozin ◽  
P. Megavarna Ezhilarasu ◽  
Z. Njitacke Tabekoueng ◽  
G. D. Leutcho ◽  
J. Kengne ◽  
...  
Keyword(s):  
Chua’S Oscillator ◽  
Hyperbolic Sine

A UNIFIED FRAMEWORK FOR SYNCHRONIZATION AND CONTROL OF DYNAMICAL SYSTEMS

1994 ◽  
Vol 04 (04) ◽  
pp. 979-998 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Chaotic Systems ◽  
Main Tool ◽  
Lyapunov Stability Theory ◽  
Asymptotical Stability ◽  
Unified Framework ◽  
Partial Synchronization ◽  
Chua’S Oscillator ◽  
And Control

In this paper, we give a framework for synchronization of dynamical systems which unifies many results in synchronization and control of dynamical systems, in particular chaotic systems. We define concepts such as asymptotical synchronization, partial synchronization and synchronization error bounds. We show how asymptotical synchronization is related to asymptotical stability. The main tool we use to prove asymptotical stability and synchronization is Lyapunov stability theory. We illustrate how many previous results on synchronization and control of chaotic systems can be derived from this framework. We will also give a characterization of robustness of synchronization and show that master-slave asymptotical synchronization in Chua’s oscillator is robust.

FINDING PARAMETERS FOR CHUA’S OSCILLATOR WHICH IS TOPOLOGICALLY CONJUGATE TO SYSTEMS WITH A SCALAR NONLINEARITY

1995 ◽  
Vol 05 (03) ◽  
pp. 895-899 ◽  
Author(s):  
CHAI WAH WU ◽  
LEON O. CHUA
Keyword(s):  
Vector Field ◽  
Large Class ◽  
Vector Fields ◽  
Colpitts Oscillator ◽  
Chua’S Oscillator ◽  
Scalar Nonlinearity

Chua’s oscillator is topologically conjugate to a large class of vector fields with a scalar non-linearity. In this letter, we give an algorithm which, given a vector field in this class, finds the parameters for Chua’s oscillator for which Chua’s oscillator is topologically conjugate to it. We illustrate this by transforming Sparrow’s system and the chaotic Colpitts oscillator into equivalent Chua’s oscillators.

Sychronisation of Chua's Oscillator via the State Observer Technique

2003 ◽  
Vol 40 (1) ◽  
pp. 36-44
Author(s):  
Xiaogen Yin ◽  
Y. J. Cao
Keyword(s):  
Control Theory ◽  
Control Systems ◽  
Chaotic Dynamics ◽  
State Observer ◽  
Dynamical Behaviour ◽  
Simple Approach ◽  
Nonlinear Circuit ◽  
Third Order ◽  
Rich Variety ◽  
Chua’S Oscillator

Chua's oscillator is a simple autonomous third-order nonlinear circuit with a rich variety of dynamical behaviour. This paper presents a simple approach to synchronisation of Chua's oscillators using a state observer in control theory, which can be used as an interesting example for educational purposes in control systems, showing the students a simple way of coping with chaotic dynamics.

High-order revivable complex-valued hyperbolic-sine-Gaussian solitons and breathers in nonlinear media with a spatial nonlocality

2018 ◽  
Vol 94 (4) ◽  
pp. 2563-2573 ◽  
Author(s):  
Zhen-Jun Yang ◽  
Shu-Min Zhang ◽  
Xing-Liang Li ◽  
Zhao-Guang Pang ◽  
Hong-Xia Bu
Keyword(s):  
High Order ◽  
Nonlinear Media ◽  
Spatial Nonlocality ◽  
Hyperbolic Sine ◽  
Gaussian Solitons ◽  
Complex Valued

scholarly journals Modified hyperbolic sine model for titanium dioxide-based memristive thin films

2018 ◽  
Vol 341 ◽  
pp. 012018
Author(s):  
Raudah Abu Bakar ◽  
Nur Syahirah Kamarozaman ◽  
Wan Fazlida Hanim Abdullah ◽  
Sukreen Hana Herman
Keyword(s):  
Thin Films ◽  
Titanium Dioxide ◽  
Hyperbolic Sine

scholarly journals Health-related factors on tobacco consumption in Turkey

2020 ◽  
Vol 50 (5) ◽  
Author(s):  
Nuray Demir ◽  
Abdulbaki Bilgic ◽  
Okan Demir ◽  
Adem Aksoy
Keyword(s):  
Prevalence Rate ◽  
Statistical Tests ◽  
Tobacco Consumption ◽  
Hurdle Model ◽  
Related Factors ◽  
Consumption Level ◽  
Double Hurdle Model ◽  
Hyperbolic Sine ◽  
Health Related ◽  
Double Hurdle

ABSTRACT: In this study, we analyzed the role of individuals’ health-related factors along with socio-demographic and economic characteristics on both the likelihood of tobacco consumption and quantity demanded levels using two competitive econometric methods: double hurdle model versus hyperbolic sine double-hurdle model. Statistical tests confirmed the dependency errors between the prevalence rate of smoking and the consumption level, whilst the inverse-hyperbolic sine double-hurdle model data fits best in describing the normalization of the data and the two data generating processes: the probability and consumption levels of cigarettes. Also, the variance-covariance of the selected model as a function of additional exogenous variables are confirmed, while the error terms between the likelihood to smoke and the consumption levels are positive and statistically significant, indicating that holding control variables fixed, the uncontrolled variables out of the system that increase the prevalence rate of smoking also boost the consumption level, or vice versa. Many individual disease variables are significant in both equations, breaking new grounds in literature for identifying how both the prevalence rate of smoking and amount have shaped.

scholarly journals Damaged behavior under plane stress

2011 ◽  
pp. 341-368
Author(s):  
Thomas Paris ◽  
Khémaïs Saanouni
Keyword(s):  
Plane Stress ◽  
Constitutive Equations ◽  
Stress Condition ◽  
Time Integration ◽  
Reference Case ◽  
Plane Stress Condition ◽  
Integration Schemes ◽  
Hyperbolic Sine ◽  
Time Integration Schemes ◽  
Fully Coupled

This paper deals with the numerical treatment of "advanced" elasto-viscoplasticdamage constitutive equations in the particular case of plane stress. The viscoplastic constitutive equations account for the mixed isotropic and kinematic non linear hardening and are fully coupled with the isotropic ductile damage. The viscous effect is indifferently described by a power function (Norton type) or an hyperbolic sine function. Different time integration schemes are used and compared to each other assuming plane stress condition, widely used when dealing with shell structures as well as to the 3D reference case.

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