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Area of Science:

  • Nonlinear Dynamics
  • Chaos Theory
  • Complex Systems

Background:

  • Deterministic chaotic systems can exhibit complex behaviors.
  • Stochastic resonance typically involves noise, but similar effects can arise in deterministic systems.
  • Understanding phase dynamics is crucial in oscillator studies.

Purpose of the Study:

  • To numerically demonstrate stochastic-resonance-like behavior in a deterministic chaotic oscillator.
  • To investigate the synchronization of phase slips with modulated external forces.
  • To elucidate the underlying dynamical mechanism of this observed phenomenon.

Main Methods:

  • Utilizing a modified Rössler system as the deterministic chaotic oscillator.
  • Driving the system with a sinusoidal external force.
  • Introducing a periodic input signal to weakly modulate the external force.

Main Results:

  • Successfully demonstrated stochastic-resonance-like behavior.
  • Observed synchronization between intermittent 2 pi phase slips and the periodic input signal.
  • Identified a boundary crisis, dependent on two bifurcation parameters, as the dynamical mechanism.

Conclusions:

  • Stochastic-resonance-like phenomena can emerge in deterministic chaotic systems without external noise.
  • Phase slip synchronization provides a novel pathway to observe such effects.
  • The boundary crisis mechanism offers a new perspective on resonance phenomena in nonlinear systems.