# Spatiotemporal chaos in terms of unstable recurrent patterns

@article{Christiansen1996SpatiotemporalCI, title={Spatiotemporal chaos in terms of unstable recurrent patterns}, author={Freddy Bugge Christiansen and Predrag Cvitanovi{\'c} and Vakhtang Putkaradze}, journal={Nonlinearity}, year={1996}, volume={10}, pages={55-70} }

Spatiotemporally chaotic dynamics of a Kuramoto - Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as an accurate guide to the high-dimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics.

## 125 Citations

### Unstable recurrent patterns in Kuramoto-Sivashinsky dynamics.

- MathematicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2008

We undertake an exploration of recurrent patterns in the antisymmetric subspace of the one-dimensional Kuramoto-Sivashinsky system. For a small but already rather "turbulent" system, the long-time…

### Analysis of chaotic saddles in high-dimensional dynamical systems: the Kuramoto-Sivashinsky equation.

- PhysicsChaos
- 2004

A novel technique is described that uses the stable manifold of a chaotic saddle to characterize the homoclinic tangency responsible for an interior crisis, a chaotic transition that results in the enlargement of a Chaos attractor.

### Intermittent chaos driven by nonlinear Alfvén waves

- Physics
- 2004

Abstract. We investigate the relevance of chaotic saddles and unstable periodic orbits at the onset of intermittent chaos in the phase dynamics of nonlinear Alfven waves by using the…

### Intermittency induced by attractor-merging crisis in the Kuramoto-Sivashinsky equation.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2005

An attractor-merging crisis in a spatially extended system exemplified by the Kuramoto-Sivashinsky equation is characterized, with the origin of this crisis-induced intermittency explained in terms of alternate switching between two chaotic saddles embedded in the merged chaotic attractor.

### Inferring symbolic dynamics of chaotic flows from persistence.

- PhysicsChaos
- 2020

This work adapts a topological data analysis technique known as persistent homology for the characterization of state space projections of chaotic trajectories and periodic orbits for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors.

### Characterization of a high-dimensional interior crisis in a nonlinear reactive-diffusion equation

- Mathematics
- 2004

### Chaotic saddles at the onset of intermittent spatiotemporal chaos.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2007

It is demonstrated that a similar mechanism is present in the damped Kuramoto-Sivashinsky equation that undergoes a transition to spatiotemporal chaos (STC) via quasiperiodicity and temporal chaos.

### Spatiotemporally periodic solutions by variational methods

- Physics
- 1999

The intriguing “Hopf’s last hope”— proposal for a theory of turbulence has significant physical meaning. The problem is how to describe chaotic/turbulent spatiotemporal patterns. Typical system…

### Sensitivity of attractor to external influences: approach by unstable periodic orbits

- Physics, Environmental Science
- 2001

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