Transient Instability and Patterns of Reactivity in Diffusive-Chemotaxis Soil Carbon Dynamics

Area of Science:

• Mathematical Biology
• Ecology
• Biophysics

Background:

• Pattern formation is crucial in biological systems, often linked to Turing instability.
• Understanding transient dynamics is key to fully characterizing pattern-forming potential.

Purpose of the Study:

• To investigate pattern formation in a bacterial chemotaxis and soil carbon dynamics model.
• To explore how transient dynamics can induce patterns outside of traditional Turing unstable regimes.

Main Methods:

• Analysis of non-spatial and spatial dynamics reactivity.
• Stability analyses and numerical continuation.
• Investigation of parameter regimes and bifurcation analysis.

Main Results:

• Pattern formation observed in Turing unstable regimes.
• Transient growth in spatially uniform states can induce patterns, especially in bistable regions of subcritical Turing bifurcations.
• Bistable regions favoring pattern formation were found in 2D but not 1D domains.

Conclusions:

• Reactivity and transient growth are significant mechanisms for pattern formation, extending beyond Turing instability.
• Geometric dimensionality plays a critical role in the emergence of multistable patterns.
• Findings have implications for modeling bacterial soil organic carbon dynamics and reaction-transport systems.