Slow passage through the Busse balloon -- predicting steps on the Eckhaus staircase

2023/09/26 by Anna Asch, Montie Avery, Asch, Anna +5 · 2 citations
Environmental Science · Earth and Planetary Sciences · Social Sciences · #Ecosystem dynamics and resilience #Earth Systems and Cosmic Evolution #Evolutionary Game Theory and Cooperation

paper · pdf · doi:10.48550/arxiv.2309.14959

Abstract

Motivated by the impact of worsening climate conditions on vegetation patches, we study dynamic instabilities in an idealized Ginzburg-Landau model. Our main results predict time instances of sudden drops in wavenumber and the resulting target states. The changes in wavenumber correspond to the annihilation of individual vegetation patches when resources are scarce and cannot support the original number of patches. Drops happen well after the primary pattern has destabilized at the Eckhaus boundary and key to distinguishing between the disappearance of 1,2, or more patches during the drop are complex spatio-temporal resonances in the linearization at the unstable pattern. We support our results with numerical simulations and expect our results to be conceptually applicable universally near the Eckhaus boundary, in particular in more realistic models.

Cited by

• The evasion of tipping: pattern formation near a Turing-fold bifurcation
• Fronts and patterns with a dynamic parameter ramp

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