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Chaos in a simple model of a delta network
Gerard Salter1, Vaughan R Voller2, Chris Paola3
1Department of Earth and Environmental Sciences, St. Anthony Falls Laboratory, University of Minnesota, Minneapolis, MN 55414; gsalter@caltech.edu.
Flux partitioning in delta networks can lead to chaotic dynamics. While precise delta configurations are unpredictable long-term, their statistical behavior, or climate, remains predictable.
Area of Science:
- Geomorphology
- Complex Systems Science
- Stratigraphy
Background:
- Flux partitioning in delta networks is crucial for land building and stratigraphy generation.
- Previous models of single bifurcations showed periodic dynamics due to channel deepening and deposition interplay.
Purpose of the Study:
- To investigate flux-partitioning dynamics in a two-bifurcation delta network model.
- To explore the potential for chaotic behavior in coupled deltaic systems.
Main Methods:
- Development of a simple numerical model with two orders of bifurcations.
- Analysis of model dynamics for sensitive dependence on initial conditions and Lyapunov exponents.
- Generation of synthetic stratigraphy to compare with natural systems.
Main Results:
- Coupling between bifurcations can induce chaotic, aperiodic yet bounded dynamics.
- The model demonstrates sensitive dependence on initial conditions, indicating long-term unpredictability.
- Periodic windows were observed, suggesting potential shifts between predictable and unpredictable states.
- Generated stratigraphy shows realistic patterns like upward fining and scale-dependent compensation.
Conclusions:
- Chaotic behavior may be widespread in geomorphic systems, imposing fundamental predictability limits.
- Delta network "weather" (specific configurations) is unpredictable long-term, but delta "climate" (statistical behavior) is predictable.
- Further improvements in delta network modeling are possible within estimated predictability horizons.
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