Tunable bimodal explorations of space from memory-driven deterministic dynamics

Maxime Hubert (1) , Stéphane Perrard (2, 3) , Matthieu Labousse (4) , Nicolas Vandewalle (5) , Yves Couder (6)

1 LITEN - Laboratoire d'Innovation pour les Technologies des Energies Nouvelles et les nanomatériaux
2 IRPHE - Institut de Recherche sur les Phénomènes Hors Equilibre
3 Physique Non-Linéaire
4 IL - Institut Langevin - Ondes et Images (UMR7587)
5 GRASP - Group for Research and Applications in Statistical Physics
6 MSC - Matière et Systèmes Complexes

We present a wave-memory-driven system that exhibits intermittent switching between two propulsion modes in free space. The model is based on a pointlike particle emitting periodically cylindrical standing waves. Submitted to a force related to the local wave-field 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.

Domaines: Dynamique Chaotique [nlin.CD]

Maxime Hubert, Stéphane Perrard, Matthieu Labousse, Nicolas Vandewalle, Yves Couder. Tunable bimodal explorations of space from memory-driven deterministic dynamics. Physical Review E , 2019, 100 (3), ⟨10.1103/PhysRevE.100.032201⟩. ⟨hal-02349244⟩