Study of a novel conservative chaotic system with special initial offset boosting behaviors

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Fractional Calculus

Background:

• Growing interest in conservative systems, yet limited research on fractional-order conservative systems.
• Need for novel chaotic systems with unique dynamical properties.

Purpose of the Study:

• To propose and analyze a novel five-dimensional fractional-order conservative chaotic system.
• To investigate its unique dynamical behaviors and physical realizability.

Main Methods:

• Adomian decomposition method for solving fractional-order differential equations.
• Analysis using phase diagrams, bifurcation diagrams, and Lyapunov exponential spectra.
• Circuit implementation on a digital signal processing (DSP) platform.

Main Results:

• Discovery of rare dynamical behaviors, including homogeneous and heterogeneous initial offset boosting.
• Identification of novel initial offset boosting with identical phase trajectory structures.
• Uncovering two key factors influencing homogeneous and heterogeneous conservative flows.

Conclusions:

• The proposed fractional-order system exhibits complex and novel dynamics.
• Physical realizability confirmed through DSP circuit implementation and experimental validation.
• The study contributes to the understanding of fractional-order chaotic systems.