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    Dynamical Analysis of a Quadratic Megastable Chaotic Oscillator and Its Application in Biometric Fingerprint Image Encryption
    (Wiley-Hindawi, 2024) Subramanian, Rajeskannan; Cicek, Serdar; Akgul, Akif; Adam, Girma; Karthikeyan, Anitha; Rajagopal, Karthikeyan
    This investigation centers on megastable systems, distinguished by their countable infinite attractors, with a particular emphasis on the Quadratic Megastable Oscillator (QMO). Unlike traditional megastable oscillators reliant on external excitation, our proposed QMO operates autonomously, contributing to its distinctiveness. Through a comprehensive exploration of the QMO, we elucidate various dynamical behaviors, enriching the understanding of its complex system dynamics. In contrast to conventional megastable oscillators, the QMO yields nested types of multiple attractors for diverse initial conditions, elegantly depicted in phase portraits. To gauge the sustainability of chaotic oscillation, we employ influential parameter bifurcation plots, providing a nuanced insight into the system's dynamical evolution. The complexity of the proposed system is further underscored by its intricate basins of attraction, accommodating an infinite number of coexisting attractors. Exploring trajectory dynamics, we observe that certain initial conditions lead trajectories to distant destinations, evading the influence of local attractors. This behavior underscores the uniqueness of the QMO and highlights its potential applications in scenarios requiring nonlocalized attractor behaviors. Taking a practical turn, the QMO is applied to biometric fingerprint image encryption, demonstrating its efficacy in real-world applications. Rigorous statistical analyses and vulnerability assessments confirm the success of the QMO in providing secure encryption within chaotic system-based frameworks. This research contributes not only to the theoretical understanding of megastable systems but also establishes the QMO as a valuable tool in encryption applications, emphasizing its robustness and versatility in complex dynamical scenarios.
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    The Effect of Using Multi-Scroll Chaotic Systems on Chaos-Based Random Number Generators' Performance
    (World Scientific Publ Co Pte Ltd, 2022) Cicek, Serdar
    Chaotic and hyper-chaotic systems are used in various engineering applications such as encryption, communication, and artificial intelligence. Also, chaotic systems are widely used in chaos-based random number generator (RNG) designs as chaotic system signals are not periodic and produce different values continuously. Since multi-scroll chaotic systems (MSCSs) produce more than one scroll, the output values can take more different values than chaotic systems. In this study, the effects of different directional values and/or different numbers of scrolls of multi-scroll chaotic systems on chaos-based random number generators' performance are investigated with NIST 800-22 (National Institute of Standards and Technology) and correlation coefficient tests. As a result of the research, it has been concluded that the use of multi-scroll chaotic systems with different directional values and/or different numbers of scrolls does not always have a direct positive effect on the performance of chaos-based random number generators. Thus, it is necessary to use a special pre-process method that will vary according to the multi-scroll chaotic system to be used for chaos-based RNG designs with good performance.
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    Öğe
    Theoretical Analysis of Smooth Nonlinear Resistor-Capacitor Shunted Josephson Junction Circuit and Its Microcontroller-Based Digital Design with Graphic LCD
    (Springer Birkhauser, 2023) Ramakrishnan, Balamurali; Ngongiah, Isidore Komofor; Cicek, Serdar; Chamgoue, Andre Cheage; Kuiate, Gaetan Fautso
    This paper reports on the theoretical analysis and microcontroller implementation of smooth nonlinear resistor-capacitor shunted Josephson junction (SNRCSJJ) circuit. The smooth nonlinear resistor is described by a cosine interference term. The stability of the equilibrium points obtained from the rate equations describing the SNRCSJJ circuit reveals the existence of saddle node and transcritical bifurcation. The hysteresis loop widths of current-voltage curves increase with the increase in the coherence parameter. Periodic behaviors, relaxation behaviors, chaotic behaviors, bistable periodic attractors, and coexisting attractors are found during the numerical analysis by varying the coherence parameter and modulation parameters of alternative current (AC). In order to use both in real engineering applications and for educational purposes, microcontroller-based digital design with graphic LCD (liquid crystal display) of the SNRCSJJ circuit is designed. The digital design results matched the simulation results.