Comment on noise and bifurcations. (English) Zbl 0925.58071
Summary: We calculate in exact form the first correction in a parameter measuring the strength of the noise to the effective potential for one-variable diffusion processes. The use of this potential to study transitions is discussed.
MSC:
37G99 | Local and nonlocal bifurcation theory for dynamical systems |
82C31 | Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics |
37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
37J40 | Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol’d diffusion |
70L05 | Random vibrations in mechanics of particles and systems |
References:
[1] | C. Meunier and A. D. Verga,J. Stat. Phys. 50:345 (1988). · Zbl 1086.37521 · doi:10.1007/BF01022998 |
[2] | R. Graham, inStochastic Processes in Nonequilibrium Systems, L. Garridoet al., eds. (Springer, 1978). |
[3] | F. Langouche, D. Roekaerts, and E. Tirapegui,Functional Integration and Semiclassical Expansions (Reidel, 1982). · Zbl 0505.28009 |
[4] | E. Tirapegui, inNew Trends in Nonlinear Dynamics and Pattern Forming Phenomena, P. Coullet and P. Huerre, eds. (Plenum Press, New York, 1990). |
[5] | E. Gozzi,Phys. Rev. D 28:1922 (1983). · doi:10.1103/PhysRevD.28.1922 |
[6] | A. J. Mckane, H. C. Luckock, and A. J. Bray,Phys. Rev. A 41:644 (1990). · doi:10.1103/PhysRevA.41.644 |
[7] | F. Langouche, D. Roekaerts, and E. Tirapegui,Physica 97A:195 (1979). |
[8] | F. Langouche, D. Roekaerts, and E. Tirapegui,Phys. Rev. D 20:419, 433 (1979). · doi:10.1103/PhysRevD.20.419 |
[9] | M. Le Bellac,Des phénomènes critiques aux champs de gauge (CNRS, 1988). |
[10] | H. Dekker,Physica 103A:55 (1980). |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.