The origin of localized patterns with a spatiotemporal oscillatory background state
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View abstract on PubMed
Summary
This summary is machine-generated.Localized patterns in oscillatory systems emerge from subcritical Turing-Hopf bifurcations, originating from homoclinic snaking. This study explains the complex spatiotemporal pattern formation via higher-order bifurcations.
Area Of Science
- Nonlinear Dynamics
- Pattern Formation
- Mathematical Biology
Background
- Spatiotemporal oscillatory backgrounds often exhibit localized patterns.
- These patterns are hypothesized to arise from bistability in supercritical Turing-Hopf modes.
- The precise origin of pattern branching remains incompletely understood.
Purpose Of The Study
- To investigate the formation of localized patterns near subcritical Turing-Hopf bifurcation points.
- To elucidate the branching mechanisms of these complex spatiotemporal patterns.
- To utilize the Gray-Scott model as a representative system for analysis.
Main Methods
- Multiple scales analysis to derive a space-time coupled amplitude equation.
- Numerical continuation to trace solution branches.
- Bifurcation analysis to identify critical points and transitions.
Main Results
- Demonstrated persistence of localized patterns under subcritical bifurcation conditions.
- Identified a novel branch on homoclinic snaking as the origin of these patterns.
- Revealed that higher-order bifurcations govern the emergence of oscillatory localized patterns.
Conclusions
- Provided new insights into the formation of complex spatiotemporal patterns.
- Offered a mechanistic explanation for oscillatory localized patterns originating from subcritical bifurcations.
- Highlighted the role of homoclinic snaking and higher-order bifurcations in pattern genesis.
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