Nonlinear dynamics and circuit realization of a new chaotic flow: A variant of Lorenz, Chen and Lü

Li, Xianfeng; Chlouverakis, K.E.; Xu, Duo

doi:10.1016/j.nonrwa.2008.04.024

Cited by 51 publications

(19 citation statements)

References 13 publications

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“…The circuit in Figure 5 has been designed following a general approach based on operational amplifiers [26,27,28,29]. The variable x, y and z of the new chaotic system (1) are the voltage across the capacitor C 1 ,C 2 and C 3 .…”

Section: Circuit Realization Of the New Chaotic Systemmentioning

confidence: 99%

A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot

Vaidyanathan¹,

Sambas²,

Mamat³

et al. 2017

Archives of Control Sciences

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A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot SUNDARAPANDIAN VAIDYANATHAN, ACENG SAMBAS, MUSTAFA MAMAT and MADA SANJAYA WS This research work proposes a new three-dimensional chaotic system with a hidden attractor. The proposed chaotic system consists of only two quadratic nonlinearities and the system possesses no critical points. The phase portraits and basic qualitative properties of the new chaotic system such as Lyapunov exponents and Lyapunov dimension have been described in detail. Finally, we give some engineering applications of the new chaotic system like circuit simulation and control of wireless mobile robot.

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Section: Circuit Realization Of the New Chaotic Systemmentioning

confidence: 99%

A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot

Vaidyanathan¹,

Sambas²,

Mamat³

et al. 2017

Archives of Control Sciences

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show abstract

“…In order to observe the effectiveness of the proposed adaptive synchronization scheme, a new simple threedimensional chaotic system [15] is employed as the slave system …”

Section: Numerical Examplesmentioning

confidence: 99%

Synchronization of Chaotic Systems with Uncertain Parameters by Adaptive Control

Chu

Leung

2010

2010 International Conference on Measuring Technology and Mechatronics Automation

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This paper addresses a unified mathematical expression describing a class of chaotic and hyper-chaotic systems, for which the problem of synchronization between different chaotic and hyper-chaotic systems with uncertain parameters is studied. Based on the Lyapunov stability theory, a novel, simple and systemic adaptive synchronization controller is designated, the analytic expression of the controller and the adaptive laws of parameters are developed. Two different chaotic systems and a hyper-chaotic system are employed as the examples to show the effectiveness of the proposed adaptive synchronization scheme. Additionally, the robustness of the proposed method and the effect of noise are investigated by measuring the mean squared error of the systems.

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“…With higher dimension, chaotic attractor occupies more space and winding complexly. The most complex attractor has much more complex output signals so that encryption effect would be better, whereas three-dimensional autonomous chaotic systems with higher fractal dimension are rare [16].…”

Section: Introductionmentioning

confidence: 99%

Image Encryption Algorithm Based on a Novel Improper Fractional-Order Attractor and a Wavelet Function Map

Zhao

Wang

Zhang

et al. 2017

Journal of Electrical and Computer Engineering

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This paper presents a three-dimensional autonomous chaotic system with high fraction dimension. It is noted that the nonlinear characteristic of the improper fractional-order chaos is interesting. Based on the continuous chaos and the discrete wavelet function map, an image encryption algorithm is put forward. The key space is formed by the initial state variables, parameters, and orders of the system. Every pixel value is included in secret key, so as to improve antiattack capability of the algorithm. The obtained simulation results and extensive security analyses demonstrate the high level of security of the algorithm and show its robustness against various types of attacks. 1 1 = + sin ( + + ) , 2 2 = − ,

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Nonlinear dynamics and circuit realization of a new chaotic flow: A variant of Lorenz, Chen and Lü

Cited by 51 publications

References 13 publications

A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot

A new three-dimensional chaotic system with a hidden attractor, circuit design and application in wireless mobile robot

Synchronization of Chaotic Systems with Uncertain Parameters by Adaptive Control

Image Encryption Algorithm Based on a Novel Improper Fractional-Order Attractor and a Wavelet Function Map

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