Chaotic Saddles in Spatiotemporal Complex Systems

author: Rodrigo A. Miranda, INPE - National Institute for Space Research
published: Dec. 3, 2007,   recorded: October 2007,   views: 342


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Chaotic transients such as chaotic saddles, strange repellers, semi-attractors, and super-transients have been observed in many deterministic systems (Kantz and Grassberger 1985; Rempel and Chian 2005; Chian, Rempel and Rogers 2006; Rempel and Chian 2007). Formulas can be derived to relate the average life time of the transient to dimensions of the chaotic transient, and to Lyapunov exponents of the flow on it.In this paper, we show that chaotic saddles are responsible for chaotic transients and intermittency in extended complex systems exemplified by a nonlinear regularized long-wave equation, relevant to fluid and plasma studies (Rempel and Chian 2007). Following a transition to spatiotemporal chaos via quasiperiodicity and temporal chaos, the intermittent time series displays random switching between regimes of temporal and spatiotemporal chaos. Before the transition to spatiotemporal chaos, we identify a spatiotemporal chaotic saddle responsible for chaotic transients that mimic the dynamics of the post-transition attractor and can be used to predict its behavior. After the transition to spatiotemporal chaos, we describe a method to identify temporal and spatiotemporal chaotic saddles responsible for the two intermittent regimes.A similar scenario has been observed in the Kuramoto-Sivashinsky equation. We suggest that this scenario can be readily found in extended dissipative dynamical systems that exhibit transient spatiotemporal chaos prior to the transition to sustained spatiotemporal chaos, which evolve from temporal chaos to spatiotemporal chaos via a crisis-like chaotic transition, e.g., pipe flows and nonlinear optical systems. In fact, this scenario has been observed in a model of ring of cardiac cells and plasma laboratory experiments of drift waves.

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