Dynamics, Circuit Design and Fractional-Order Form of a Modified Rucklidge Chaotic System

Sambas, Aceng; Vaidyanathan, Sundarapandian; Mamat, Mustafa; Sanjaya, W. S. Mada; Yuningsih, Siti Hadiaty; Zakaria, Kiki; Subiyanto, .

doi:10.1088/1742-6596/1090/1/012038

Cited by 4 publications

(6 citation statements)

References 33 publications

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“…Table 1 outlines existing systems, i.e. Lorenz [7] (and the modified [10,18]), Rossler [8], Rikitake [9] (and the modified [21]), Rucklidge [14],…”

Section: Lyapunov Exponents and Kaplan-yorke Dimensionmentioning

confidence: 99%

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A New 6D Chaotic Generator: Computer Modelling and Circuit Design

Kopp¹,

Kopp²

2022

Int. j. eng. technol. innov.

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The objective of this study aims at using the Matlab-Simulink environment and the LabVIEW software environment to build computer models of a six-dimensional (6D) chaotic dynamic system. For the fixed system’s parameters, the spectrum of Lyapunov exponents and the Kaplan-York dimension are calculated. The presence of two positive Lyapunov exponents demonstrates the hyperchaotic behavior of the system. The fractional Kaplan-York dimension indicates the fractal structure of strange attractors. An active control method is extended to achieve global chaotic synchronization of two identical novel 6D chaotic systems with unknown system parameters. Based on the results obtained in Matlab-Simulink and LabVIEW models, a chaotic signal generator for the 6D chaotic system is implemented in the MultiSim environment. The experimental results show that the chaotic behavior simulation in the MultiSim environment is similar to those in the Matlab-Simulink and LabVIEW models. The simulation results demonstrate that the Pecora-Carroll method is a simple way of chaotic masking and signal decoding.

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“…Table 1 outlines existing systems, i.e. Lorenz [7] (and the modified [10,18]), Rossler [8], Rikitake [9] (and the modified [21]), Rucklidge [14],…”

Section: Lyapunov Exponents and Kaplan-yorke Dimensionmentioning

confidence: 99%

“…The development of new electronic dynamic chaos generators has been accelerating recently. Electronic chaos generators are based on Rössler equations [8], Rikitake equations [9], modified Lorentz equations [10][11][12][13], and Rucklidge equations [14].…”

Section: Introductionmentioning

confidence: 99%

A New 6D Chaotic Generator: Computer Modelling and Circuit Design

Kopp¹,

Kopp²

2022

Int. j. eng. technol. innov.

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show abstract

“…Thus, the 8D chaotic system (3) with unknown system parameter R is globally and exponentially stabilized for all initial conditions by the adaptive control law (7) and the parameter update law (12). Let us consider the adaptive synchronization of identical 8D chaotic systems with unknown system parameter R .…”

Section: Adaptive Control Of the 8d Chaotic Systemmentioning

confidence: 99%

“…Due to the work [4] the creation of electronic chaos generators was stimulated. Electronic generators of chaos immediately appeared based on Rössler equations [5,6], Rikitake equations [7], modified Lorentz equations [8][9][10][11], Rucklidge equations [12]. Recently, new systems with hyperchaotic oscillations have been developed such as Liu systems [13][14], Chen systems [15] and new modifications of the Lorentz equations [16][17] and Rikitake equations [18][19][20].…”

Section: Introductionmentioning

confidence: 99%

Computer Modelling and Circuit Design of a new 8D Chaotic System

Kopp¹,

Kopp²

2022

Preprint

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In this paper, Matlab-Simulink and LabView models are constructed for a new nonlinear dynamic system of equations in an eight-dimensional (8D) phase space. For fixed parameters of the 8D dynamical system, the spectrum of Lyapunov exponents and the Kaplan-York dimension are calculated. The presence of two positive Lyapunov exponents demonstrates the hyperchaotic behavior of the 8D dynamical system. The fractional Kaplan-York dimension indicates the fractal structure of strange attractors. We have shown that an adaptive controller is used to stabilize the novel 8D chaotic system with unknown system parameters. An active control method is derived to achieve global chaotic synchronization of two identical novel 8D chaotic systems with unknown system parameters. Based on the results obtained in Matlab-Simulink and LabView models, a chaotic signal generator for the 8D chaotic system is implemented in the Multisim environment. The results of chaotic behavior simulation in the Multisim environment show similar behavior when comparing simulation results in Matlab-Simulink and LabView models.

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“…The literature on chaotic systems is rich and diverse, featuring numerous well-known chaotic systems that have been extensively studied. Some of these include Lorenz system [4], Rössler equations [5]- [6], Rikitake equations [7], modified Lorentz equations [8], and Rucklidge equations [9]. Some noteworthy systems producing hyperchaotic oscillations have been developed, such as the Liu systems [10]- [11], Chen systems [12], and new modifications of the Lorentz equations [13]- [14] and Rikitake equations [15]- [16].…”

Section: Introductionmentioning

confidence: 99%

A new 7D memristor-based hyperchaotic system and its application to secret information transmission

Kopp

2024

Preprint

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This work presents a new seven-dimensional (7D) chaotic system based on a fluxcontrolled memristor, which we consider in two versions. The first version of a 7D memristive chaotic system describes self-excited attractors. In the second version, in a 7D memristive chaotic system, hidden attractors can arise by adjusting the values of one constant parameter. A study was conducted on both types of innovative 7D dynamic systems to determine Lyapunov exponents, construct bifurcation diagrams, and identify equilibrium points and the corresponding stability conditions for each system. As a result of computer modeling of 7D hyperchaotic systems in Matlab-Simulink, phase portraits were obtained for self-excited and hidden strange attractors. Finally, electronic circuits for new 7D chaos generators with different types of attractors were built using Multisim software, which showed behavior similar to the Matlab-Simulink models. The synchronization problem for both identical 7D hyperchaotic memristive systems was investigated using the active control method. For practical applications, a method of chaotic encryption and decryption of an information signal was developed and numerically tested.

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Dynamics, Circuit Design and Fractional-Order Form of a Modified Rucklidge Chaotic System

Cited by 4 publications

References 33 publications

A New 6D Chaotic Generator: Computer Modelling and Circuit Design

A New 6D Chaotic Generator: Computer Modelling and Circuit Design

Computer Modelling and Circuit Design of a new 8D Chaotic System

A new 7D memristor-based hyperchaotic system and its application to secret information transmission

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