Localized states with nontrivial symmetries: Localized labyrinthine patterns

Area of Science:

• Physics
• Complex Systems
• Pattern Formation

Background:

• Self-organized patterns and localized states are common in nature.
• Trivial symmetry patterns (stripes, hexagons) are well-understood.
• Disordered patterns with nontrivial symmetries, like labyrinthine patterns, appear in diverse physical systems.

Purpose of the Study:

• To report the observation of stable localized disordered patterns in spatially extended dissipative systems.
• To characterize these structures as isolated labyrinths within a homogeneous steady state.
• To explain the formation mechanism via a pinning-depinning transition.

Main Methods:

• Analysis of two- and three-dimensional localized structures.
• Construction of a partial bifurcation diagram.
• Illustration using Swift-Hohenberg-type equations and established models from plant ecology, nonlinear optics, and reaction-diffusion systems.

Main Results:

• Stable localized disordered patterns, specifically isolated labyrinths, were observed.
• These structures are embedded in a homogeneous steady state.
• A pinning-depinning transition was identified as the underlying mechanism.

Conclusions:

• Localized disordered patterns can form stably in dissipative systems.
• The pinning-depinning transition provides a framework for understanding their formation.
• Findings are relevant to diverse fields including nonlinear optics, plant ecology, and reaction-diffusion systems.