The influence of noise on scalings for in-out intermittency

Details The influence of noise on scalings for in-out intermittency The influence of noise on scalings for in-out intermittency

2001-05-12

arxiv.org/abs/nlin/0105033v1

Nonlinear Sciences

Chaotic Dynamics

Submitted to Physical Review E, also available at http://www.eurico.web.com

Scientific paper

10.1103/PhysRevE.64.066204

We study the effects of noise on a recently discovered form of intermittency, referred to as in-out intermittency. This type of intermittency, which reduces to on-off in systems with a skew product structure, has been found in the dynamics of maps, ODE and PDE simulations that have symmetries. It shows itself in the form of trajectories that spend a long time near a symmetric state interspersed with short bursts away from symmetry. In contrast to on-off intermittency, there are clearly distinct mechanisms of approach towards and away from the symmetric state, and this needs to be taken into account in order to properly model the long time statistics. We do this by using a diffusion-type equation with delay integral boundary condition. This model is validated by considering the statistics of a two-dimensional map with and without the addition of noise.

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