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Fairy circles and temporal periodic patterns in the delayed plant-sulfide feedback model
Xin Wei1, Jianjun Paul Tian2, Jiantao Zhao1
1School of Mathematical Sciences, Heilongjiang University, Harbin, Heilongjiang 150080, China.
Mathematical Biosciences and Engineering : MBE
|November 1, 2024
Summary
Time delays in salt marsh feedback systems can cause temporal or spatial patterns. Understanding these patterns, like fairy circles, reveals ecological resilience mechanisms.
Area of Science:
- Ecology
- Mathematical Biology
- Systems Biology
Background:
- Intertidal salt marshes exhibit complex spatial patterns, such as fairy circles.
- Plant-sulfide feedback systems are crucial for salt marsh ecosystems.
- Self-regulatory mechanisms with time delays can influence ecological dynamics.
Purpose of the Study:
- To investigate the impact of time delays in self-regulatory mechanisms on plant-sulfide feedback systems in salt marshes.
- To analyze the stability and bifurcation properties of a reaction-diffusion model incorporating time delays.
- To understand the formation of spatial patterns like fairy circles.
Main Methods:
- Development and analysis of a functional reaction-diffusion model.
- Stability analysis of the positive steady state.
- Derivation of conditions for Hopf bifurcations using normal form theory.
- Numerical simulations to observe pattern formation.
Main Results:
- A critical time delay value was identified, distinguishing between temporal and spatial pattern formation.
- Time delays exceeding the critical value lead to asymptotic temporal periodic patterns.
- Time delays below the critical value result in asymptotic spatial homogeneous patterns.
- Transient fairy circles were observed for all time delays, with variations in type and ring structures.
Conclusions:
- Time delays in self-regulatory mechanisms significantly influence pattern formation in salt marsh ecosystems.
- Fairy circle patterns serve as indicators of underlying ecological mechanisms and resilience.
- The study provides insights into the role of time delays in ecological stability and pattern dynamics.
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