Interactions of \((m,n)\) and \((m+1,n)\) modes with real eigenvalues: a dynamic transition approach

Normal forms, center manifold theory, bifurcation theory for infinite-dimensional dissipative dynamical systems (37L10) Nonlinear evolution equations (47J35) Pattern formations in context of PDEs (35B36)

Cites Work

Pattern formation in Rayleigh-Bénard convection
Pattern formation and dynamic transition for magnetohydrodynamic convection
Dynamic transitions and pattern formations for a Cahn-Hilliard model with long-range repulsive interactions
Dynamic bifurcation and stability in the Rayleigh-Bénard convection
Infinite-dimensional dynamical systems in mechanics and physics.
Attractor bifurcation theory and its applications to Rayleigh-Bénard convection
Dynamic bifurcation and transition in the Rayleigh-Bénard convection with internal heating and varying gravity
Dynamical transitions of a low-dimensional model for Rayleigh-Bénard convection under a vertical magnetic field
Turing instability and dynamic phase transition for the Brusselator model with multiple critical eigenvalues
Hopf bifurcations and transitions of two-dimensional quasi-geostrophic flows
Transitions in stochastic non-equilibrium systems: efficient reduction and analysis
On the stability and transition of the Cahn-Hilliard/Allen-Cahn system
On the viscous instabilities and transitions of two-layer model with a layered topography
On the stability and bifurcation of the non-rotating Boussinesq equation with the Kolmogorov forcing at a low Péclet number
Dynamical transition theory of hexagonal pattern formations
Transitions and bifurcations in couple stress fluid saturated porous media using a thermal non-equilibrium model
Dynamical transition and bifurcation of hydromagnetic convection in a rotating fluid layer
Dynamic transitions and bifurcations of 1D reaction-diffusion equations: the non-self-adjoint case
Pattern formations of 2D Rayleigh-Bénard convection with no-slip boundary conditions for the velocity at the critical length scales
Dynamic transitions for quasilinear systems and Cahn-Hilliard equation with Onsager mobility
Phase Transition Dynamics
Transitions of zonal flows in a two-layer quasi-geostrophic ocean model
Dynamic transition analysis for activator-substrate system

This page was built for publication: Interactions of \((m,n)\) and \((m+1,n)\) modes with real eigenvalues: a dynamic transition approach