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2009•SIAM Journal on Applied Dynamical SystemsOpen access

On the Implementation of the 0–1 Test for Chaos

Georg A. Gottwald, Ian Melbourne

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Abstract

In this paper we address practical aspects of the implementation of the 0–1 test for chaos in deterministic systems. In addition, we present a new formulation of the test which significantly increases its sensitivity. The test can be viewed as a method for distilling a binary quantity from the power spectrum. The implementation is guided by recent results from the theoretical justification of the test as well as by exploring better statistical methods for determining the binary quantities. We give several examples to illustrate the improvement.

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What this paper is about

In this paper we address practical aspects of the implementation of the 0–1 test for chaos in deterministic systems. In addition, we present a new formulation of the test which significantly increases its sensitivity. The test can be viewed as a method for distilling a binary quantity from the power spectrum. The implementation is guided by recent results from the theoretical justification of the test as well as by exploring better statistical methods for determining the binary quantities. We give several examples to illustrate the improvement.

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OpenAlex reports 512 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

In this paper we address practical aspects of the implementation of the 0–1 test for chaos in deterministic systems. In addition, we present a new formulation of the test which significantly increases its sensitivity. The test can be viewed as a method for distilling a binary quantity from the power spectrum. The implementation is guided by recent results from the theoretical justification of the test as well as by exploring better statistical methods for determining the binary quantities. We give several examples to illustrate the improvement.

Key concepts: CHAOS (operating system), Binary number, Computer science, Test (biology), Sensitivity (control systems), Mathematics, Arithmetic, Electronic engineering

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