Interaction of a Hopf bifurcation and a symmetry-breaking bifurcation: stochastic potential and spatial correlations
The multivariate master equation for a general reaction-diffusion system is solved perturbatively in the stationary state, in a range of parameters in which a symmetry-breaking bifurcation and a Hopf bifurcation occur simultaneously. The stochastic potential U is, in general, not analytic. However, in the vicinity of the bifurcation point and under precise conditions on the kinetic constants, it is possible to define a fourth-order expansion of U around the bifurcating fixed point. Under these conditions, the domains of existence of different attractors, including spatiotemporal structures as well as the spatial correlations of the fluctuations around these attractors, are determined analytically. The role of fluctuations in the existence and stability of the various patterns is pointed out.
- Research Organization:
- Universite Pierre et Marie Curie, Paris (France)
- OSTI ID:
- 6279425
- Journal Information:
- J. Stat. Phys.; (United States), Vol. 53:3-4
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
CHEMICAL REACTIONS
STATISTICAL MODELS
DIFFUSION
MULTIVARIATE ANALYSIS
CORRELATIONS
DYNAMICS
EIGENVALUES
FLUCTUATIONS
HAMILTONIANS
MATHEMATICAL MANIFOLDS
MATHEMATICAL SPACE
PARTIAL DIFFERENTIAL EQUATIONS
PERTURBATION THEORY
STATISTICAL MECHANICS
STOCHASTIC PROCESSES
SYMMETRY BREAKING
VECTOR FIELDS
DIFFERENTIAL EQUATIONS
EQUATIONS
MATHEMATICAL MODELS
MATHEMATICAL OPERATORS
MATHEMATICS
MECHANICS
QUANTUM OPERATORS
SPACE
STATISTICS
VARIATIONS
657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics