Analysis of 4D autonomous system with volume-expanding phase space

摘要

This paper investigates the dynamics of four-dimensional autonomous oscillator with antiparallel diodes. A rare phenomenon of volume-expanding phase space is observed from the proposed model, and the only equilibrium point at the origin is found to be a repeller. Systems of this kind pave the way for the better understanding of repellers. In addition, the oscillator possesses extremely rich dynamical behaviors, including 2-tori, 3-tori (triple tori), limit cycles, chaos and hyperchaos. These dynamical behaviors are characterized with the help of the Lyapunov spectrum, bifurcation diagram, recurrence analysis, Poincar, surface of section, 0-1 test etc., Period doubling and torus breakdown to chaos are the predominant routes observed in the system for different parametric choices. The results of the real-time circuit are quite compatible with the numerical predictions.