2025/07/10 by Yumeng Wang, Bin Chen, Runze Lan +1 · 2 citations
Mathematics · Physics and Astronomy · #Classical mechanics #Fractional Differential Equations Solutions #Hamiltonian (control theory) #Hamiltonian system #Mathematics #Multistability #Nonlinear system #Numerical methods for differential equations #Order (exchange) #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Scroll #Statistical physics
paper · doi:10.1088/1402-4896/adedcc
published in Physica Scripta 100(8), 085210 (IOP Publishing)
openalex publication_date 2025/07/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
Abstract In this study, a novel five-dimensional fractional-order conservative system with extreme multistability and controllable multiscroll dynamics is proposed. The system’s non-linear behavior is investigated using classical dynamical analysis. Numerical simulations reveal high sensitivity to initial conditions, with phase trajectories exhibiting distinct topological features such as expansion, contraction, rotation, symmetry, and spatial displacement. Interestingly, even with constant Hamiltonian energy, changes in initial conditions lead to significantly different phase space structures - highlighting the complex dependence of the system on its starting state. Transient dynamics is also observed, governed by the system’s fractional order and characterized by switching among different phase trajectories over time. A piecewise function is introduced to realize, for the first time, a controllable multi-scroll mechanism in a fractional-order conservative system, allowing the generation of an arbitrary number of scrolls. The system’s feasibility is further demonstrated through hardware implementation on a digital signal processor (DSP), with results consistent with numerical simulations. These findings offer a solid basis for future applications in secure communications and nonlinear engineering systems.