# How long do numerical chaotic solutions remain valid

@article{Sauer1997HowLD, title={How long do numerical chaotic solutions remain valid}, author={Tim Sauer and Celso Grebogi and James A. Yorke}, journal={Physical Review Letters}, year={1997}, volume={79}, pages={59-62} }

Dynamical conditions for the loss of validity of numerical chaotic solutions of physical systems are already understood. However, the fundamental questions of {open_quotes}how good{close_quotes} and {open_quotes}for how long{close_quotes} the solutions are valid remained unanswered. This work answers these questions by establishing scaling laws for the shadowing distance and for the shadowing time in terms of physically meaningful quantities that are easily computable in practice. The scaling…

## 110 Citations

Pseudo-Deterministic Chaotic Systems

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It is shown that unstable-dimension variability can occur in wide parameter regimes of chaotic systems with an invariant subspace such as systems of coupled chaotic oscillators, and this paper investigates this phenomenon by investigating a class of deterministic models.

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- 2014

A method of true orbit generation that allowed us to perform exact simulations of discrete-time dynamical systems defined by one-dimensional piecewise linear and linear fractional maps with integer coefficients by generalizing the method proposed by Saito and Ito is introduced.

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Using 1200 CPUs of the National Supercomputer TH-A1 and a parallel integral algorithm based on the 3500th-order Taylor expansion and the 4180-digit multiple precision data, we have done a reliable…

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- 2008

This work identifies regions in state space of conservative and dissipative chaotic systems that allow statements about future states or the predictability. This is done using two kinds of local…

Statistics of shadowing time in nonhyperbolic chaotic systems with unstable dimension variability.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2004

It is shown that the probability distribution of the shadowing time contains two distinct scaling behaviors: an algebraic scaling for short times and an exponential scaling for long times, and the small-time algebraic behavior appears to be universal.

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