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Shadowing in hidden attractors. / Kamal, N. K.; Varshney, V.; Shrimali, M. D.; Prasad, A.; Kuznetsov, N. V.; Leonov, G. A.

In: Nonlinear Dynamics, Vol. 91, No. 4, 01.03.2018, p. 2429-2434.

Research output: Contribution to journal › Article › peer-review

Harvard

Kamal, NK, Varshney, V, Shrimali, MD, Prasad, A, Kuznetsov, NV & Leonov, GA 2018, 'Shadowing in hidden attractors', Nonlinear Dynamics, vol. 91, no. 4, pp. 2429-2434. https://doi.org/10.1007/s11071-017-4022-z

APA

Kamal, N. K., Varshney, V., Shrimali, M. D., Prasad, A., Kuznetsov, N. V., & Leonov, G. A. (2018). Shadowing in hidden attractors. Nonlinear Dynamics, 91(4), 2429-2434. https://doi.org/10.1007/s11071-017-4022-z

Vancouver

Kamal NK, Varshney V, Shrimali MD, Prasad A, Kuznetsov NV, Leonov GA. Shadowing in hidden attractors. Nonlinear Dynamics. 2018 Mar 1;91(4):2429-2434. https://doi.org/10.1007/s11071-017-4022-z

Author

Kamal, N. K. ; Varshney, V. ; Shrimali, M. D. ; Prasad, A. ; Kuznetsov, N. V. ; Leonov, G. A. / Shadowing in hidden attractors. In: Nonlinear Dynamics. 2018 ; Vol. 91, No. 4. pp. 2429-2434.

BibTeX

@article{2a20f6be9e4b4cf5ac2cfe617c47e6ab,
title = "Shadowing in hidden attractors",
abstract = "Hidden attractors found in physical systems are different from self-exited attractors and may have a small basin of attraction. The issue of shadowing in these attractors using dynamical noise is discussed. We have particularly considered two classes of dynamical systems which have hidden attractors in their state space. In one of the systems, there is no fixed point but only a hidden attractor in the state space, while in the other, the system has one unstable fixed point along with a hidden attractor in the state space. The effect of dynamical noise on these dynamical systems is studied by using the Hausdorff distance between the noisy and deterministic attractors. It appears that, up to some threshold value of noise, the noisy trajectory completely shadows the noiseless trajectory in these attractors which is quite different from the results of self-exited attractors. We compare the results of hidden chaotic attractors with the self-exited chaotic attractors.",
keywords = "Dynamical system, Hidden attractor, Shadowing",
author = "Kamal, {N. K.} and V. Varshney and Shrimali, {M. D.} and A. Prasad and Kuznetsov, {N. V.} and Leonov, {G. A.}",
year = "2018",
month = mar,
day = "1",
doi = "10.1007/s11071-017-4022-z",
language = "English",
volume = "91",
pages = "2429--2434",
journal = "Nonlinear Dynamics",
issn = "0924-090X",
publisher = "Springer Nature",
number = "4",

}

RIS

TY - JOUR

T1 - Shadowing in hidden attractors

AU - Kamal, N. K.

AU - Varshney, V.

AU - Shrimali, M. D.

AU - Prasad, A.

AU - Kuznetsov, N. V.

AU - Leonov, G. A.

PY - 2018/3/1

Y1 - 2018/3/1

N2 - Hidden attractors found in physical systems are different from self-exited attractors and may have a small basin of attraction. The issue of shadowing in these attractors using dynamical noise is discussed. We have particularly considered two classes of dynamical systems which have hidden attractors in their state space. In one of the systems, there is no fixed point but only a hidden attractor in the state space, while in the other, the system has one unstable fixed point along with a hidden attractor in the state space. The effect of dynamical noise on these dynamical systems is studied by using the Hausdorff distance between the noisy and deterministic attractors. It appears that, up to some threshold value of noise, the noisy trajectory completely shadows the noiseless trajectory in these attractors which is quite different from the results of self-exited attractors. We compare the results of hidden chaotic attractors with the self-exited chaotic attractors.

AB - Hidden attractors found in physical systems are different from self-exited attractors and may have a small basin of attraction. The issue of shadowing in these attractors using dynamical noise is discussed. We have particularly considered two classes of dynamical systems which have hidden attractors in their state space. In one of the systems, there is no fixed point but only a hidden attractor in the state space, while in the other, the system has one unstable fixed point along with a hidden attractor in the state space. The effect of dynamical noise on these dynamical systems is studied by using the Hausdorff distance between the noisy and deterministic attractors. It appears that, up to some threshold value of noise, the noisy trajectory completely shadows the noiseless trajectory in these attractors which is quite different from the results of self-exited attractors. We compare the results of hidden chaotic attractors with the self-exited chaotic attractors.

KW - Dynamical system

KW - Hidden attractor

KW - Shadowing

UR - http://www.scopus.com/inward/record.url?scp=85040040990&partnerID=8YFLogxK

UR - http://www.mendeley.com/research/shadowing-hidden-attractors

U2 - 10.1007/s11071-017-4022-z

DO - 10.1007/s11071-017-4022-z

M3 - Article

AN - SCOPUS:85040040990

VL - 91

SP - 2429

EP - 2434

JO - Nonlinear Dynamics

JF - Nonlinear Dynamics

SN - 0924-090X

IS - 4

ER -

ID: 35275187