Quasiperiodic Oscillations and Low-Frequency Chaos in a Degenerate Duffing Oscillator

The paper investigates the mechanisms responsible for the emergence of quasiperiodic oscillations and low-frequency chaos in a degenerate harmonic Duffing oscillator by analyzing bifurcation diagrams constructed with respect to the amplitude of an external force. This approach makes it possible to reveal a number of previously hidden dynamical effects, including the appearance of an additional chaotic regime at relatively small force amplitudes; the splitting of the main chaotic regime by extremely narrow quasiperiodic windows associated with subharmonic and superharmonic quasiperiodic oscillations; the formation of periodic regimes related to the existence of a three-point attractor; and the manifestation of subharmonic and superharmonic oscillations at certain values of the force amplitude. Numerical simulations are performed using the Adams–Bashforth–Moulton finite-difference method implemented as a predictor–corrector scheme with a variable time step.