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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.

Memristor-based oscillators are of recent interest, and hence, in this paper, we introduce a new Wien bridge oscillator with a fractional-order memristor. The novelty of the proposed oscillator is the multistability feature and the wide range of fractional orders for which the system shows chaos. We have investigated the various dynamical properties of the proposed oscillator and have presented them in detail. The oscillator is then realized using off-the-shelf components, and the results are compared with that of the numerical results. A combination synchronization scheme is proposed which uses more than one driver systems to synchronize with one response system. Indeed, we use two different techniques where the first one consists of splitting the transmitted signals into two parts where each part is loaded in different drive systems, while the second one consists of dividing time into different intervals and loading the signals in different drive systems. Such techniques improve the antiattack capability of the systems when used for secure communication.

This paper introduces a fractional order memristor no equilibrium (FOMNE) chaotic system and investigates its adaptive sliding mode synchronization. Firstly the dynamic properties of the integer order memristor no equilibrium system are analyzed. The fractional order memristor no equilibrium system is then derived from the integer order model. Lyapunov exponents and bifurcation with fractional order are investigated. An adaptive sliding mode control algorithm is derived to globally synchronize the identical fractional order memristor systems and genetically optimized fractional order PID controllers are designed and used to synchronize the FOMNE systems. Finally the fractional order memristor no equilibrium system is realized using FPGA.