Diffusive oscillators capture the pulsating states of deformable particles.

Area of Science:

• Physics
• Complex Systems
• Nonlinear Dynamics

Background:

• Deformable particles with pulsating sizes exhibit dynamical arrest due to repulsion at high densities.
• Diffusive oscillators are models for collective behavior in various physical and biological systems.

Purpose of the Study:

• To investigate the emergence of dynamical arrest and spiral waves in a model of diffusive oscillators.
• To understand the underlying mechanisms of arrest and synchronization in these systems.
• To compare the dynamics of diffusive oscillators with deformable particles.

Main Methods:

• Modeling diffusive oscillators with periodic driving of internal states.
• Analytical coarse-graining techniques.
• Comparison of collective dynamics between diffusive oscillators and deformable particles.

Main Results:

• Dynamical arrest emerges in diffusive oscillators due to the discrete nature of internal states, creating an effective energy landscape.
• Competition between arrest and synchronization promotes spiral waves, analogous to pulsating states of deformable particles.
• Analytical derivations rationalize spiral formation via rotational invariance and elucidate the role of hydrodynamic fluctuations.

Conclusions:

• The discrete nature of internal states in diffusive oscillators can lead to complex emergent behaviors like arrest and spiral waves, similar to systems with inter-particle repulsion.
• The study provides a theoretical framework for understanding collective dynamics and emergent patterns in oscillatory systems.
• This work bridges the gap between abstract oscillator models and physical systems like deformable particles.