Basin-filling Peano omega-branches and structural stability of a chaotic attractor

Ueda, Yoshisuke

doi:10.1587/nolta.5.252

Cited by 5 publications

(1 citation statement)

References 7 publications

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“…Instead, chaotic attractors have physical reality in the sense that their geometrical structures can be reproducibly observed with a probability of unity. These observations appear to be consistent with Ueda's theory of chaos [13,14], wherein chaotic dynamical behavior represents a manifestation of random transitions, triggered by experimental perturbations or numerical roundoff, between (infinitely many) unstable periodic orbits accompanying (infinitely many) homoclinic points in the chaotic attractors [15]. Ueda referred to such dynamical behavior as randomly transitional oscillations [13].…”

Section: Introductionsupporting

confidence: 77%

Chaotic time series prediction by noisy echo state network

Shinozaki

Miyano

Horio

2020

NOLTA

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We have applied noisy echo state networks to the short-term forecasting of hyperchaotic and chaotic time series. The hyperchaotic time series were generated using the augmented Lorenz equations as a star network of Q nonidentical Lorenz systems and a fourdimensional Lorenz system. The echo state networks were used mainly in the recursive forecasting mode, wherein the output value of the network, i.e., the predicted value, at the current time step was recursively fed back to the input node at the next time step of prediction. The addition of external noise to the reservoir network has been found to considerably improve the fidelity of the geometrical structures of the chaotic attractors reconstructed from the predicted time series. We discuss these observations on the basis of Ueda's theory of chaos.

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Section: Introductionsupporting

confidence: 77%