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Flux dynamics in an annular long Josephson junction is studied. Three maintopics are covered. The first is chaotic flux dynamics and its prediction viaMelnikov integrals. It turns out that DC current bias cannot induce chaoticflux dynamics, while AC current bias can. The existence of a common root to theMelnikov integrals is a necessary condition for the existence of chaotic fluxdynamics. The second topic is on the components of the global attractor and thebifurcation in the perturbation parameter measuring the strength of loss, biasand irregularity of the junction. The global attractor can contain co-existinglocal attractors e.g. a local chaotic attractor and a local regular attractor.In the infinite dimensional phase space setting, the bifurcation is verycomplicated. Chaotic attractors can appear and disappear in a random fashion.Three types of attractors (chaos, breather, spatially uniform and temporallyperiodic attractor) are identified. The third topic is ratchet effect. Ratcheteffect can be achieved by a current bias field which corresponds to anasymmetric potential, in which case the flux dynamics is ever lasting chaotic.When the current bias field corresponds to a symmetric potential, the fluxdynamics is often transiently chaotic, in which case the ratchet effectdisappears after sufficiently long time.

ON THE CHAOTIC FLUX DYNAMICS IN A LONG JOSEPHSON JUNCTION