Multistability and Bifurcation Analysis of a Novel 3D Jerk System: Electronic Circuit Design, FPGA Implementation, and Image Cryptography Scheme

Bonny, Talal; Vaidyanathan, Sundarapandian; Sambas, Aceng; Benkouider, Khaled; Nassan, Wafaa Al; Naqaweh, Omar

doi:10.1109/access.2023.3299171

Cited by 6 publications

(3 citation statements)

References 33 publications

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“…In their work, conditions for the appearance of Hopf and fold bifurcations were constructed. A 3-D jerk system with three quadratic nonlinear terms was presented by Bonny et al [1], and the dynamical properties of the system were demonstrated by utilizing phase portraits, bifurcation diagrams, Lyapunov exponents, multistability, and coexisting attractors.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis with self-excited and hidden attractors for a chaotic jerk system

Rasul,

Salih

2024

J. Math. Computer Sci.

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This paper is devoted to investigating the local bifurcation of a chaotic jerk system. The local stability of equilibrium points is analyzed, as well as the existence of transcritical bifurcation at the origin. For the proposed jerk system, the Hopf and Zero-Hopf bifurcations are investigated at the origin. Moreover, a zero-Hopf equilibrium point at the origin is characterized for the system. By using the averaging theory of first order, a limit cycle can be bifurcated from the zero-Hopf equilibrium located at the origin. Liapunov quantities techniques are used to investigate the cyclicity of the system. It is shown that three limit cycles can be bifurcated from the origin. Finally, both self-excited chaotic attractors and hidden chaotic attractors are studied for special cases of the chaotic jerk systems using bifurcation diagrams, Lyapunov exponents, and cross-sections. All results reported in this study have been obtained using Maple software.

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Section: Introductionmentioning

confidence: 99%

Bifurcation analysis with self-excited and hidden attractors for a chaotic jerk system

Rasul,

Salih

2024

J. Math. Computer Sci.

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“…Logistic map, Henon map, Henon 3-D map and Lorenz discrete map are discrete-time systems. In addition, the chaotic systems presented in previous work have been implemented using different techniques such as electronic circuits [ 13 , 14 ], FPGA implementation [ 15 – 18 ]and memristor-based circuits [ 19 ].…”

Section: Introductionmentioning

confidence: 99%

Comparative analysis and FPGA realization of different control synchronization approaches for chaos-based secured communication systems

Bonny,

Al Nassan,

Sambas

2024

PLoS ONE

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Synchronization of the chaotic systems has attracted much attention in recent years due to its vital applications in secured communication systems. In this paper, an implementation and comparative analysis of two different control approaches for synchronization between two identical four-dimensional hyperchaotic systems is presented. The two control approaches are the Adaptive nonlinear controller and the linear optimal quadratic regulator LQR. To demonstrate the effectiveness of each controller, the numerical simulation is presented using Matlab/Simulink and the control law is derived. The performance of the proposed controllers is compared based on four factors; response time, squared error integration, energy applied from the controller, and cost function. To measure the robustness of the control approaches, the performance factors are compared when there is a change in system parameters and a variation in the initial conditions. Then the proposed synchronization methods are implemented on the FPGA platform to demonstrate the utilized resources on Field Programmable Gate Array (FPGA) hardware platform and the operation speed. Finally, to generalize the results of the comparison, the study is implemented for the synchronization of another secured communication system consisting of two identical three-dimensional chaotic. The experimental results show that the LQR method is more effective than the Adaptive controller based on the performance factors we propose. Moreover, the LQR is much simpler to implement on hardware and requires fewer resources on the FPGA.

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“…Bonny et al in [13] have investigated a 3-D jerk system with three quadratic nonlinear terms. In their work, they studied the dynamical properties of the system using bifurcation diagrams, Lyapunov exponents, multistability and coexisting attractors.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation analysis with chaotic attractor for a special case of jerk system

Rasul,

Salih

2024

Phys. Scr.

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This paper is focused on investigating the local bifurcations of a special type of chaotic jerk system. The occurrence and non-occurrence of saddle-node, transcritical and pitchfork bifurcations at the origin, as well as the Hopf and Zero-Hopf bifurcations when n = 3, are examined. For the proposed system, the parameters that lead to a zero-Hopf equilibrium point at the origin are characterized. Additionally, it has been demonstrated that employing the ﬁrst-order averaging theory results in the emergence of a single periodic solution branching out from the zero-Hopf equi-librium located at the origin. Furthermore, the focus quantities method is utilized to explore the periodicity of the system. This method helps to determine the number of periodic solutions that can emerge from the Hopf point. Due to the computational load for computing singular quantities, only three singular quantities were found. Under speciﬁc conditions, it is shown that three periodic solutions can emerge from the origin of the system. Finally, the chaotic attractors of the system are also studied.

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Multistability and Bifurcation Analysis of a Novel 3D Jerk System: Electronic Circuit Design, FPGA Implementation, and Image Cryptography Scheme

Cited by 6 publications

References 33 publications

Bifurcation analysis with self-excited and hidden attractors for a chaotic jerk system

Bifurcation analysis with self-excited and hidden attractors for a chaotic jerk system

Comparative analysis and FPGA realization of different control synchronization approaches for chaos-based secured communication systems

Bifurcation analysis with chaotic attractor for a special case of jerk system

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