Multipeaked probability distributions of recurrence times

Area of Science:

• Physics
• Nonlinear Dynamics
• Chaos Theory

Background:

• Previous studies on autonomous chaotic systems reported only monotonic decaying distributions for recurrence times.
• Existing models often simplify phase space, overlooking complex trajectory behaviors.

Purpose of the Study:

• To determine probabilities of recurrence time within finite, physically meaningful phase space subsets.
• To investigate recurrence time distributions in three distinct autonomous chaotic systems.

Main Methods:

• Analysis of recurrence time probabilities in phase space subsets.
• Examination of three autonomous chaotic systems: three-peaked potential scattering, connected billiards, and Lorenz equations.

Main Results:

• Identified multipeaked probability distributions for recurrence times, deviating from expected monotonic decay.
• Observed that discrete peaks correspond to specific trajectory subsets, including those with integer loops.
• Found similarities between these distributions and those in driven stochastically resonant systems.

Conclusions:

• Autonomous chaotic systems can exhibit non-monotonic recurrence time distributions.
• The presence of discrete peaks highlights the importance of considering detailed trajectory structures within phase space.
• These findings necessitate a re-evaluation of recurrence time analysis in nondriven chaotic systems.