Tunable bimodal explorations of space from memory-driven deterministic dynamics

TL;DR

This paper introduces a wave-memory driven system where a particle exhibits intermittent switching between two propulsion modes, driven by chaotic dynamics, with potential implications for understanding search strategies in biological systems.

Contribution

The study presents a novel wave-memory system demonstrating bimodal propulsion and chaos-driven switching, advancing understanding of memory effects in dynamical systems.

Findings

System exhibits erratic switching between linear and diffusive motion.

Bimodal dynamics are driven by Shil'nikov chaos.

Memory controls the time spent in each propulsion mode.

Abstract

We present a wave-memory driven system that exhibits intermittent switching between two propulsion modes in free space. The model is based on a point-like particle emitting periodically cylindrical standing waves. Submitted to a force related to the local wavefield gradient, the particle is propelled, while the wave field stores positional information on the particle trajectory. For long memory, the linear motion is unstable and we observe erratic switches between two propulsive modes : linear motion and diffusive motion. We show that the bimodal propulsion and the stochastic aspect of the dynamics at long time are generated by a Shil'nikov chaos. The memory of the system controls the fraction of time spent in each phase. The resulting bimodal dynamics shows analogies with intermittent search strategies usually observed in living systems of much higher complexity.