On the Rucklidge time-delayed chaotic system for nonlinear double convection: Adaptive control, synchronization and LabVIEW implementation

N. Bernardara *, A. Lafaurie, F. I. Saad

Faculté des Sciences, Université de Nice Sophia Antipolis, parc Valrose, 06108 Nice, France


There is great interest shown in the literature in the discovery of chaotic motion and oscillations in nonlinear dynamical systems arising in physics, chemistry, biology, and engineering. Chaotic systems have many important applications in science and engineering. This paper discusses the Rucklidge chaotic system for nonlinear double convection and time-delayed Rucklidge chaotic system. When the convection takes place in a fluid layer rotating uniformly about a vertical axis and in the limit of tall thin rolls, convection in an imposed vertical magnetic field and convection in a rotating fluid layer are both modeled by Rucklidge’s three-dimensional system of ordinary differential equations, which produces chaotic solutions. This paper starts with a detailed description of the Rucklidge’s nonlinear double convection system and the parameter values for which the Rucklidge system exhibits chaotic behavior. Next, an adaptive feedback controller is designed for the global chaos control of the time delayed Rucklidge chaotic system with unknown parameters. Furthermore, an adaptive feedback controller is designed for the global chaos synchronization of the identical Rucklidge chaotic system with its time-delayed Chaotic System. All the main results derived in this work are illustrated with MATLAB simulations. Finally, the circuit design of the novel A 3-D chaotic system is implemented in LABVIEW to validate the theoretical chaotic model.


Chaos, Chaos control, Chaos synchronization, Rucklidge system, Double convection, Fluid mechanics, Circuit simulation, LABVIEW implementation

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Article history

Received 3 February 2019, Received in revised form 5 May 2019, Accepted 7 May 2019

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Bernardara N, Lafaurie A, and Saad FI (2019). On the Rucklidge time-delayed chaotic system for nonlinear double convection: Adaptive control, synchronization and LabVIEW implementation. Annals of Electrical and Electronic Engineering, 2(6): 10-19

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