Table 1 A list of the prediction time duration of RC systems for different chaotic systems at the given precision threshold.

From: Synchronization of non-smooth chaotic systems via an improved reservoir computing

Systems

N

p

r

Precision threshold

Duration (or steps)

Units of Lyapunov time

Hénon

235

0.0469

0.6088

\(5\times 10^{-3}\)

\(60\,(21^{*}, 21^{\#})\)

\(25\,(9^{*}, 9^{\#})\)

Ikeda

544

0.0173

0.1426

\(5\times 10^{-5}\)

\(60\,(19^{*}, 19^{\#})\)

\(8\,(3^{*}, 3^{\#})\)

Chua

274

0.0454

0.1629

\(5\times 10^{-5}\)

\(40\,(18.78^{*}, 11.66^{\#})\)

\(13\,(6^{*}, 4^{\#})\)

PLUC

147

0.0421

0.1993

\(5\times 10^{-3}\)

\(20\,(0.66^{*}, 0.28^{\#})\)

\(31\,(1^{*}, 0^{\#})\)

Lorenz

606

0.0115

0.9207

\(5\times 10^{-4}\)

\(15\,(10.04^{*}, 6.64^{\#})\)

\(20\,(13^{*}, 9^{\#})\)

Rössler

734

0.0411

0.5876

\(5\times 10^{-8}\)

\(110\,(22.96^{*},31.88^{\#})\)

\(9\,(2^{*},3^{\#})\)

  1. Here, symbols \(*\) and \(\#\) represents the prediction time using the empirical and randomly-selected parameters, respectively. Lyapunov time is defined as the reciprocal of the largest Lyapunov exponent of a system. Each prediction duration of improved RC systems averages 50 realizations in the SADE algorithm, and the listed optimally-selected parameters are one of 50 experiments.