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    • Complexity, Dynamics, Control, and Applications of Nonlinear Systems with Multistability
    Authors: Viet-Thanh Pham; Sundarapandian Vaidyanathan; Tomasz Kapitaniak;  Advisor: -;  Co-Author: - (2020)

    Multistability is a critical property of nonlinear dynamical systems, where a variety of phenomena such as coexisting attractors can appear for the same parameters but with different initial conditions. The flexibility in the system’s performance can be achieved without changing parameters. Complex dynamics have been observed in multistable systems, and we have witnessed systems with multistability in numerous fields ranging across physics, biology, chemistry, electronics, and mechanics, as well as reported applications in oscillators and secure communications. It is now well established from a variety of studies that multistable systems are very sensitive to both random noise and perturbations. Numerous studies such as open-loop control, feedback control, adaptive control, intellig...
    • A Novel Mega-stable Chaotic Circuit
    Authors: Viet-Thanh PHAM; Dalia Sami ALI; Nadia M.G. AL-SAIDI; Karthikeyan RAJAGOPAL; Fawaz E. ALSAADI; Sajad JAFARI;  Advisor: -;  Co-Author: - (2020)

    In recent years designing new multistable chaotic oscillators has been of noticeable interest. A multistable system is a double-edged sword which can have many benefits in some applications while in some other situations they can be even dangerous. In this paper, we introduce a new multistable two-dimensional oscillator. The forced version of this new oscillator can exhibit chaotic solutions which makes it much more exciting. Also, another scarce feature of this system is the complex basins of attraction for the infinite coexisting attractors. Some initial conditions can escape the whirlpools of nearby attractors and settle down in faraway destinations. The dynamical properties of this new system are investigated by the help of equilibria analysis, bifurcation diagram, Lyapunov expo...