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Updated: Jun 28, 2026
06:42
Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
Eckhaus instability and homoclinic snaking
A Bergeon1, J Burke, E Knobloch
1IMFT UMR CNRS 5502-UPS UFR MIG, 31062 Toulouse Cedex, France.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 13, 2008
Summary
Homoclinic snaking, a phenomenon in bistable systems, describes oscillating localized states. This study examines how snaking terminates in finite domains, relating it to Eckhaus instability.
Area of Science:
- Nonlinear dynamics
- Pattern formation
- Fluid dynamics
Background:
- Homoclinic snaking involves oscillations of spatially localized states in bistable systems.
- This behavior is observed in the subcritical Swift-Hohenberg equation and doubly diffusive convection.
- In unbounded systems, snaking can continue indefinitely, resembling periodic states.
Purpose of the Study:
- To investigate the termination of homoclinic snaking in finite and periodic domains.
- To identify factors influencing termination points of snaking branches.
- To explore the relationship between snaking termination and Eckhaus instability.
Main Methods:
- Analysis of homoclinic snaking in spatially extended systems.
- Examination of the subcritical Swift-Hohenberg equation and doubly diffusive convection.
- Investigating the transition to spatially periodic states and their instabilities.
Main Results:
- Snaking branches terminate when the localized state length approaches the domain size.
- Termination points are influenced by domain size and system parameters.
- The termination is linked to the Eckhaus instability of the spatially periodic state.
Conclusions:
- Homoclinic snaking in finite domains exhibits turnover behavior.
- Understanding termination mechanisms is crucial for predicting pattern formation in confined systems.
- The study provides insights into the interplay between localized structures and global instabilities.
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