Deterministic stochastic resonance in a Rössler oscillator.

Area of Science:

• Nonlinear Dynamics
• Chaos Theory
• Signal Processing

Background:

• Deterministic systems can display complex behaviors, including intermittent phase slips in periodically forced oscillators like the Rössler system.
• Stochastic resonance is a phenomenon where noise enhances signal detection, typically in nonlinear systems.

Purpose of the Study:

• To investigate stochastic resonance-like behavior in a deterministic Rössler oscillator.
• To demonstrate the synchronization of phase slips with weak external signals.
• To determine the conditions for optimal signal enhancement through chaotic fluctuations.

Main Methods:

• Numerical simulations of a periodically forced Rössler oscillator.
• Analysis of inter-slip intervals and signal-to-noise ratio.
• Derivation of phase slip rate based on boundary crisis and unstable-unstable pair bifurcation.

Main Results:

• Phase slips in the Rössler oscillator synchronize statistically with a weak modulating signal.
• Maximum synchronization is achieved at an optimal intensity of chaotic fluctuations.
• Stochastic resonance-like behavior is observed across various parameter choices.
• An optimal signal frequency for maximum resonance was identified.
• Derived phase slip rate and theoretical models align with numerical simulations.
• Weak signals mixed with noise can be maximally enhanced by adjusting chaotic fluctuations.

Conclusions:

• Deterministic systems can exhibit stochastic resonance-like phenomena, enhancing weak signal detection.
• Optimizing chaotic fluctuations is key to synchronizing phase slips and maximizing signal enhancement.
• The findings offer insights into signal processing in complex dynamical systems.