Thursday, May 22

3:00 PM-5:00 PM Ballroom I - Level B

Noise and Heteroclinic Phenomena

Homoclinic and heteroclinic cycles are common in nonlinear dynamics, usually arising in global bifurcations but also occurring, in a structurally stable way, in some systems with symmetry. Introduction of noise to systems that exhibit homoclinic/heteroclinic phenomena can result in qualitative changes in the dynamics, with the appearance of new characteristic timescales and the masking of chaotic behaviour being common. Because deterministic equations usually are not precise descriptions of physical systems, it is important in applications to know which features of the deterministic dynamics persist under the addition of noise. This minisymposium looks at the effect of noise on a number of systems that have homoclinic, heteroclinic, or related phenomena. Various approaches will be discussed, including methods based on stochastic differential equations, Fokker-Planck equations, and numerical integration/simulation.

Organizers: Vivien Kirk, University of Auckland, New Zealand; and Emily Stone, Utah State University

10:00 Probability Densities for Qualitatively Modified Dynamics
Rachel Kuske, Tufts University; George Papanicolaou, Stanford University; and Steve Baer, Arizona State University
10:30 Noise-Controlled Dynamics in Normal Forms
Grant Lythe, Los Alamos National Laboratory; and Steve Tobias, University of Colorado, Boulder
11:00 Noisy Cycles, the Sequel
Emily F. Stone, Organizer; and Dieter Armbruster, Arizona State University
11:30 A Heteroclinic Network with Noise
Vivien Kirk, Organizer; and Mary Silber, Northwestern University

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TMP, 4/4/97