A Skeleton of Collision Dynamics: Hierarchical Network Structure among Even-Symmetric Steady Pulses in Binary Fluid Convection

DOI10.1137/15M1010968zbMath1375.76179MaRDI QIDQ2808176

Yasumasa Nishiura, Takeshi Watanabe, Makoto Iima

Publication date: 20 May 2016

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

bifurcationcollision dynamicsbinary fluid mixturelocalized structureabsolute and convective instability and stabilityhierarchical network structure

Mathematics Subject Classification ID

Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Free convection (76R10) Forced convection (76R05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Infinite-dimensional dissipative dynamical systems (37L99)

Related Items (6)

Optimizing the control of transition to turbulence using a Bayesian method ⋮ Toward Convectons in the Supercritical Regime: Homoclinic Snaking in Natural Doubly Diffusive Convection ⋮ A probabilistic protocol for the assessment of transition and control ⋮ Matched asymptotic expansion approach to pulse dynamics for a three-component reaction-diffusion system ⋮ Three-dimensional doubly diffusive convectons: instability and transition to complex dynamics ⋮ Near-onset dynamics in natural doubly diffusive convection

Cites Work

• Unnamed Item
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• Exponential asymptotics of localised patterns and snaking bifurcation diagrams
• Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation
• Isolas of 2-pulse solutions in homoclinic snaking scenarios
• Localized periodic patterns for the non-symmetric generalized Swift-Hohenberg equation
• Homoclinic snaking near the surface instability of a polarisable fluid
• Spontaneous formation of travelling localized structures and their asymptotic behaviour in binary fluid convection
• The emergence of a coherent structure for coherent structures: localized states in nonlinear systems
• Exponential asymptotics of homoclinic snaking
• The Soret Effect: A Review of Recent Experimental Results
• Fully localised nonlinear energy growth optimals in pipe flow
• Scattering of traveling spots in dissipative systems
• LOCALIZED PATTERNS AND FRONTS IN NONEQUILIBRIUM SYSTEMS
• Three-dimensional spatially localized binary-fluid convection in a porous medium
• Three-dimensional doubly diffusive convectons: instability and transition to complex dynamics
• Localized States in an Extended Swift–Hohenberg Equation
• Travelling convectons in binary fluid convection
• Spatially localized binary-fluid convection
• The stability of finite amplitude cellular convection and its relation to an extremum principle

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