Analysis and electronic circuit implementation of an integer- and fractional-order four-dimensional chaotic system with offset boosting and hidden attractors

A new four-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit implementation.

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Controlling and Synchronization of Hyper Chaotic System Based on T-S Fuzzy Theory and Its Electronic Circuit Implementation

Journal of Computational and Theoretical Nanoscience ◽

10.1166/jctn.2015.4317 ◽

2015 ◽

Vol 12 (11) ◽

pp. 4043-4055

Author(s):

Cheng-Hsiung Yang ◽

You-Jhong Chen

Keyword(s):

Chaotic System ◽

Electronic Circuit ◽

Fuzzy Theory ◽

Circuit Implementation ◽

Electronic Circuit Implementation

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A Novel Cubic–Equilibrium Chaotic System with Coexisting Hidden Attractors: Analysis, and Circuit Implementation

Journal of Circuits System and Computers ◽

10.1142/s0218126618500664 ◽

2017 ◽

Vol 27 (04) ◽

pp. 1850066 ◽

Cited By ~ 36

Author(s):

Viet-Thanh Pham ◽

Christos Volos ◽

Sajad Jafari ◽

Tomasz Kapitaniak

Keyword(s):

Chaotic System ◽

Autonomous System ◽

Chaotic Systems ◽

Electronic Circuit ◽

Complex Dynamics ◽

Three Dimensional ◽

Chaotic Attractors ◽

Circuit Implementation ◽

Hidden Attractors ◽

Dynamical Properties

Chaotic systems with a curve of equilibria have attracted considerable interest in theoretical researches and engineering applications because they are categorized as systems with hidden attractors. In this paper, we introduce a new three-dimensional autonomous system with cubic equilibrium. Fundamental dynamical properties and complex dynamics of the system have been investigated. Of particular interest is the coexistence of chaotic attractors in the proposed system. Furthermore, we have designed and implemented an electronic circuit to verify the feasibility of such a system with cubic equilibrium.

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A New Chaotic System Family Dynamics Analysis and Circuit Implementation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.392.232 ◽

2013 ◽

Vol 392 ◽

pp. 232-236

Author(s):

Shu Min Duan ◽

Guo Zeng Wu

Keyword(s):

Chaotic System ◽

Electronic Circuit ◽

Physical Phenomenon ◽

Three Dimensional ◽

Dynamics Analysis ◽

Circuit Implementation ◽

Parallel Lines ◽

New Chaotic System ◽

Dynamical Properties ◽

Electronic Circuit Implementation

A new three-dimensional chaotic system is presented in this paper. Some basic dynamical Properties of this chaotic system are investigated by means of Poincaré mapping, Lyapunov exponents and bifurcation diagram. The dynamical behaviours of this system are proved not only by performing numerical simulation and brief theoretical analysis but also by conducting an electronic circuit implementation. It is new physical phenomenon that the Poincaré mapping of this system is a group of parallel lines.

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Analysis and electronic circuit implementation of an integer-and fractional-order Shimizu-Morioka system

Revista Mexicana de Física ◽

10.31349/revmexfis.67.061401 ◽

2021 ◽

Vol 67 (6 Nov-Dec) ◽

Author(s):

François Kapche Tagne ◽

Guillaume Honoré KOM ◽

Marceline Motchongom Tingue ◽

Pierre Kisito Talla ◽

V. Kamdoum Tamba

Keyword(s):

Numerical Simulations ◽

Fractional Order ◽

Close Agreement ◽

Electronic Circuit ◽

Dynamical Behavior ◽

Chaotic Attractors ◽

Transient Chaos ◽

Circuit Implementation ◽

Bifurcation Structures ◽

Electronic Circuit Implementation

The dynamics of an integer-order and fractional-order Lorenz like system called Shimizu-Morioka system is investigated in this paper. It is shown thatinteger-order Shimizu-Morioka system displays bistable chaotic attractors, monostable chaotic attractors and coexistence between bistable and monostable chaotic attractors. For suitable choose of parameters, the fractional-order Shimizu-Morioka system exhibits bistable chaotic attractors, monostable chaotic attractors, metastable chaos (i.e. transient chaos) and spiking oscillations. The bifurcation structures reveal that the fractional-order derivative affects considerably the dynamics of Shimizu-Morioka system. The chain fractance circuit is used to designand implement the integer- and fractional-order Shimizu-Morioka system in Pspice. A close agreement is observed between PSpice based circuit simulations and numerical simulations analysis. The results obtained in this work were not reported previously in the interger as well as in fractional-order Shimizu-Morioka system and thus represent an important contribution which may help us in better understanding of the dynamical behavior of this class of systems.

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Circuit Implementation Synchronization between Two Modified Fractional-Order Lorenz Chaotic Systems via a Linear Resistor and Fractional-Order Capacitor in Parallel Coupling

Mathematical Problems in Engineering ◽

10.1155/2021/6771261 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8 ◽

Cited By ~ 1

Author(s):

Juan Liu ◽

Xuefeng Cheng ◽

Ping Zhou

Keyword(s):

Fractional Order ◽

Chaotic System ◽

Chaos Synchronization ◽

Chaotic Systems ◽

Electronic Circuit ◽

Chaotic Attractors ◽

Circuit Implementation ◽

Lorenz Chaotic System ◽

Simulation Results ◽

Synchronization Scheme

In this study, a modified fractional-order Lorenz chaotic system is proposed, and the chaotic attractors are obtained. Meanwhile, we construct one electronic circuit to realize the modified fractional-order Lorenz chaotic system. Most importantly, using a linear resistor and a fractional-order capacitor in parallel coupling, we suggested one chaos synchronization scheme for this modified fractional-order Lorenz chaotic system. The electronic circuit of chaos synchronization for modified fractional-order Lorenz chaotic has been given. The simulation results verify that synchronization scheme is viable.

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