Analysis, Control, Synchronization and SPICE Implementation of a Novel 4-D Hyperchaotic Rikitake Dynamo System without Equilibrium
Chaos theory has wide applications and its importance can be seen by the voluminous publications on various applications in several branches of science, commerce and engineering. Control, tracking or regulation and synchronization of different types of chaotic systems are importance areas of resea...
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doaj-9cf4f6e7d13642a8a9f272ac92a4ce042020-11-24T22:09:16ZengEastern Macedonia and Thrace Institute of TechnologyJournal of Engineering Science and Technology Review1791-23771791-23772014-11-0182232244Analysis, Control, Synchronization and SPICE Implementation of a Novel 4-D Hyperchaotic Rikitake Dynamo System without EquilibriumS. Vaidyanathan0Ch. K. Volos1V. -T. Pham2Research and Development Centre, Vel Tech University, Avadi, Chennai-600062, Tamil Nadu, India.Department of Physics, Aristotle University of Thessaloniki, Thessaloniki, GR-54124, Greece.School of Electronics and Telecommunications, Hanoi University of Science and Technology, Hanoi, Vietnam.Chaos theory has wide applications and its importance can be seen by the voluminous publications on various applications in several branches of science, commerce and engineering. Control, tracking or regulation and synchronization of different types of chaotic systems are importance areas of research in the control literature and various methods have been adopted over the past few decades for tackling these research problems. Also, the discovery of novel chaotic and hyperchaotic systems in various applications, their qualitative properties and the control of such systems are also important research areas in chaos theory. This paper announces a novel 4-D hyperchaotic Rikitake dynamo system, which is derived by adding a state feedback control to the famous 3-D Rikitake two-disk dynamo system (1958). The frequent and irregular reversals of the Earth’s magnetic field inspired a number of early studies involving electrical currents within the Earth’s molten core. One of the first such models to exhibit reversals was Rikitake’s two-disk dynamo system (Rikitake, 1958). This paper discusses the qualitative properties of the novel hyperchaotic Rikitake dynamo system. We note that the novel hyperchaotic Rikitake dynamo system has no equilibrium points. The Lyapunov exponents of the hyperchaotic Rikitake dynamo system are found as �! = 0.09136, �! = 0.02198, �! = 0 and �! = −2.11190. The Kaplan-Yorke fractional dimension of the novel hyperchaotic Rikitake dynamo system is found as �!" = 3.05367. Next, this paper discusses control and synchronization of the novel hyperchaotic Rikitake dynamo system with unknown parameters using adaptive control method. The main results are established using Lyapunov stability theory and numerically illustrated using MATLAB. Finally, for the 4-D novel hyperchaotic system, an electronic circuit realization in SPICE has been described to confirm the feasibility of the theoretical hyperchaotic Rikitake dynamo model.http://www.jestr.org/downloads/Volume8Issue2/fulltext82292015.pdfChaoschaotic systemshyperchaoshyperchaotic systemsadaptive controlchaos synchronizationcircuit simulation. ____________________________ |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
S. Vaidyanathan Ch. K. Volos V. -T. Pham |
spellingShingle |
S. Vaidyanathan Ch. K. Volos V. -T. Pham Analysis, Control, Synchronization and SPICE Implementation of a Novel 4-D Hyperchaotic Rikitake Dynamo System without Equilibrium Journal of Engineering Science and Technology Review Chaos chaotic systems hyperchaos hyperchaotic systems adaptive control chaos synchronization circuit simulation. ____________________________ |
author_facet |
S. Vaidyanathan Ch. K. Volos V. -T. Pham |
author_sort |
S. Vaidyanathan |
title |
Analysis, Control, Synchronization and SPICE Implementation of a Novel 4-D Hyperchaotic Rikitake Dynamo System without Equilibrium |
title_short |
Analysis, Control, Synchronization and SPICE Implementation of a Novel 4-D Hyperchaotic Rikitake Dynamo System without Equilibrium |
title_full |
Analysis, Control, Synchronization and SPICE Implementation of a Novel 4-D Hyperchaotic Rikitake Dynamo System without Equilibrium |
title_fullStr |
Analysis, Control, Synchronization and SPICE Implementation of a Novel 4-D Hyperchaotic Rikitake Dynamo System without Equilibrium |
title_full_unstemmed |
Analysis, Control, Synchronization and SPICE Implementation of a Novel 4-D Hyperchaotic Rikitake Dynamo System without Equilibrium |
title_sort |
analysis, control, synchronization and spice implementation of a novel 4-d hyperchaotic rikitake dynamo system without equilibrium |
publisher |
Eastern Macedonia and Thrace Institute of Technology |
series |
Journal of Engineering Science and Technology Review |
issn |
1791-2377 1791-2377 |
publishDate |
2014-11-01 |
description |
Chaos theory has wide applications and its importance can be seen by the voluminous publications on various
applications in several branches of science, commerce and engineering. Control, tracking or regulation and
synchronization of different types of chaotic systems are importance areas of research in the control literature and
various methods have been adopted over the past few decades for tackling these research problems. Also, the discovery
of novel chaotic and hyperchaotic systems in various applications, their qualitative properties and the control of such
systems are also important research areas in chaos theory. This paper announces a novel 4-D hyperchaotic Rikitake
dynamo system, which is derived by adding a state feedback control to the famous 3-D Rikitake two-disk dynamo
system (1958). The frequent and irregular reversals of the Earth’s magnetic field inspired a number of early studies
involving electrical currents within the Earth’s molten core. One of the first such models to exhibit reversals was
Rikitake’s two-disk dynamo system (Rikitake, 1958). This paper discusses the qualitative properties of the novel
hyperchaotic Rikitake dynamo system. We note that the novel hyperchaotic Rikitake dynamo system has no equilibrium
points. The Lyapunov exponents of the hyperchaotic Rikitake dynamo system are found as �! = 0.09136, �! =
0.02198, �! = 0 and �! = −2.11190. The Kaplan-Yorke fractional dimension of the novel hyperchaotic Rikitake
dynamo system is found as �!" = 3.05367. Next, this paper discusses control and synchronization of the novel
hyperchaotic Rikitake dynamo system with unknown parameters using adaptive control method. The main results are
established using Lyapunov stability theory and numerically illustrated using MATLAB. Finally, for the 4-D novel
hyperchaotic system, an electronic circuit realization in SPICE has been described to confirm the feasibility of the
theoretical hyperchaotic Rikitake dynamo model. |
topic |
Chaos chaotic systems hyperchaos hyperchaotic systems adaptive control chaos synchronization circuit simulation. ____________________________ |
url |
http://www.jestr.org/downloads/Volume8Issue2/fulltext82292015.pdf |
work_keys_str_mv |
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