Chaos suppression instigated by a hyperbolic sine nonlinearity in the Chen system

2021 ◽  
Author(s):  
Paulo C. Rech
Keyword(s):  
Chen System ◽  
Chaos Suppression ◽  
Hyperbolic Sine

Chaos Suppression in Fractional order Permanent Magnet Synchronous Generator in Wind Turbine Systems

2017 ◽  
Vol 6 (2) ◽  
Author(s):  
Karthikeyan Rajagopal ◽  
Anitha Karthikeyan ◽  
Prakash Duraisamy
Keyword(s):  
Permanent Magnet ◽  
Fractional Order ◽  
Dynamic Properties ◽  
Synchronous Generator ◽  
Adaptive Controller ◽  
Control Technique ◽  
Order Model ◽  
Permanent Magnet Synchronous Generator ◽  
Chaos Suppression ◽  
Fractional Order Model

AbstractIn this paper we investigate the control of three-dimensional non-autonomous fractional-order uncertain model of a permanent magnet synchronous generator (PMSG) via a adaptive control technique. We derive a dimensionless fractional order model of the PMSM from the integer order presented in the literatures. Various dynamic properties of the fractional order model like eigen values, Lyapunov exponents, bifurcation and bicoherence are investigated. The system chaotic behavior for various orders of fractional calculus are presented. An adaptive controller is derived to suppress the chaotic oscillations of the fractional order model. As the direct Lyapunov stability analysis of the robust controller is difficult for a fractional order first derivative, we have derived a new lemma to analyze the stability of the system. Numerical simulations of the proposed chaos suppression methodology are given to prove the analytical results derived through which we show that for the derived adaptive controller and the parameter update law, the origin of the system for any bounded initial conditions is asymptotically stable.

Chaos Anti-Synchronization between Chen System and Lu System

2014 ◽  
Vol 631-632 ◽  
pp. 710-713 ◽  
Author(s):  
Xian Yong Wu ◽  
Hao Wu ◽  
Hao Gong
Keyword(s):  
Chaotic Systems ◽  
Sufficient Conditions ◽  
Lyapunov Theory ◽  
State Variables ◽  
Chen System ◽  
System Parameters ◽  
Control Scheme ◽  
Error Dynamics ◽  
The Stability ◽  
Different Chaotic Systems

Anti-synchronization of two different chaotic systems is investigated. On the basis of Lyapunov theory, adaptive control scheme is proposed when system parameters are unknown, sufficient conditions for the stability of the error dynamics are derived, where the controllers are designed using the sum of the state variables in chaotic systems. Numerical simulations are performed for the Chen and Lu systems to demonstrate the effectiveness of the proposed control strategy.

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 Study on Chaotic Fault Tolerant Synchronization Control Based on Adaptive Observer

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Dongming Chen ◽  
Xinyu Huang ◽  
Tao Ren
Keyword(s):  
Secure Communication ◽  
Chaotic Systems ◽  
Fault Tolerant ◽  
Sufficient Conditions ◽  
Adaptive Observer ◽  
Synchronization Control ◽  
Slave System ◽  
Chen System ◽  
Master System ◽  
Abrupt Faults

Aiming at the abrupt faults of the chaotic system, an adaptive observer is proposed to trace the states of the master system. The sufficient conditions for synchronization of such chaotic systems are also derived. Then the feasibility and effectiveness of the proposed method are illustrated via numerical simulations of chaotic Chen system. Finally, the proposed synchronization schemes are applied to secure communication system successfully. The experimental results demonstrate that the employed observer can manage real-time fault diagnosis and parameter identification as well as states tracing of the master system, and so the synchronization of master system and slave system is achieved.

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 Adaptive Projective Synchronization between Two Different Fractional-Order Chaotic Systems with Fully Unknown Parameters

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Liping Chen ◽  
Shanbi Wei ◽  
Yi Chai ◽  
Ranchao Wu
Keyword(s):  
Fractional Order ◽  
Chaotic Systems ◽  
Projective Synchronization ◽  
Control Law ◽  
Unknown Parameters ◽  
Chen System ◽  
Fractional Order Differential Equations ◽  
Response Systems ◽  
The Stability ◽  
Adaptive Control Law

Projective synchronization between two different fractional-order chaotic systems with fully unknown parameters for drive and response systems is investigated. On the basis of the stability theory of fractional-order differential equations, a suitable and effective adaptive control law and a parameter update rule for unknown parameters are designed, such that projective synchronization between the fractional-order chaotic Chen system and the fractional-order chaotic Lü system with unknown parameters is achieved. Theoretical analysis and numerical simulations are presented to demonstrate the validity and feasibility of the proposed method.

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