Using Floquet theory to unravel far-from equilibrium dynamics in reaction-diffusion systems

Area of Science:

• Theoretical and computational study of reaction-diffusion systems.
• Focus on spatiotemporal dynamics in biological signaling networks.

Background:

• Reaction kinetics and diffusion interplay to create diverse spatiotemporal behaviors.
• Cell contraction dynamics are controlled by the Rho-GEF-Myosin signaling network.

Purpose of the Study:

• To theoretically and computationally characterize spatiotemporal dynamics in a reaction-diffusion system.
• To investigate the Floquet-Turing-diffusion-driven-instability (FTDDI) phenomenon.

Main Methods:

• Dual hybrid dynamical systems approach.
• Numerical bifurcation analysis to identify stability regions and limit cycles.
• Floquet theory to classify spatiotemporal dynamics and FTDDI.

Main Results:

• Identified distinct spatiotemporal dynamics in both periodic and bistable regimes.
• Characterized FTDDI, where diffusion destabilizes limit cycles, leading to spatial patterns.
• In bistable regimes, diffusion can lead to classical Turing instability or FTDDI, resulting in diverse patterns like waves and pulses.

Conclusions:

• FTDDI is a key mechanism driving complex pattern formation in reaction-diffusion systems.
• Findings provide theoretical insights into spatiotemporal dynamics in biological, chemical, and ecological systems.
• The study elucidates how diffusion influences temporal stability to create spatial complexity.