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Is that Really Hidden? The Presence of Complex Fixed-Points in Chaotic Flows with No Equilibria

School of Electronics and Telecommunications, Hanoi University of Science and Technology, 01 Dai Co Viet, Hanoi, Vietnam

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Sajad Jafari

Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875–4413, Iran

Author for correspondence.

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Christos Volos

Physics Department, Aristotle University of Thessaloniki, Thessaloniki, GR–54124, Greece

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Xiong Wang

Department of Electronic Engineering, City University of Hong Kong, Hong Kong SAR, P. R. China

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, and

S. Mohammad Reza Hashemi Golpayegani

Biomedical Engineering Department, Amirkabir University of Technology, Tehran 15875–4413, Iran

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https://doi.org/10.1142/S0218127414501466Cited by:69 (Source: Crossref)

Abstract

In this letter we investigate the role of complex fixed-points in finding hidden attractors in chaotic flows with no equilibria. If these attractors could be found by starting the trajectory in the neighborhood of complex fixed-points, maybe it would be better not to call them hidden.

Keywords:

References

V. O. Bragin et al. , J. Comp. Syst. Sci. Int. 50 , 511 ( 2014 ) . Crossref, Web of Science, Google Scholar
U. Chaudhuri and A. Prasad , Phys. Lett. A 378 , 713 ( 2014 ) . Crossref, Web of Science, Google Scholar
W. G. Hoover , Phys. Rev. E 51 , 759 ( 1995 ) . Crossref, Web of Science, Google Scholar
S. Jafari and J. Sprott , Chaos Solit. Fract. 57 , 79 ( 2013 ) . Crossref, Web of Science, Google Scholar
S. Jafari , J. Sprott and S. Golpayegani , Phys. Lett. A 377 , 699 ( 2013 ) . Crossref, Web of Science, Google Scholar
M. A. Kiselevaet al., Discontinuity and Complexity in Nonlinear Physical Systems, Nonlinear Systems and Complexity 6 (Springer International Publishing, 2014) pp. 287–304. Crossref, Google Scholar
N. V. Kuznetsov , G. A. Leonov and V. I. Vagaitsev , IFAC Proc. 4 , 29 ( 2010 ) . Crossref, Google Scholar
N. V. Kuznetsov et al. , Proc. 8th Int. Conf. Inform. Contr., Automat. Robot. 4 , 279 ( 2011 ) . Google Scholar
N. V. Kuznetsov , G. A. Leonov and S. M. Seledzhi , IFAC Proc. 18 , 2506 ( 2011 ) . Crossref, Google Scholar
G. A. Leonov and N. V. Kuznetsov , Dokl. Math. 84 , 475 ( 2011 ) . Crossref, Web of Science, Google Scholar
G. A. Leonov and N. V. Kuznetsov , IFAC Proc. 18 , 2494 ( 2011 ) . Crossref, Google Scholar
G. A. Leonov et al. , Trans. Syst. Contr. 6 , 54 ( 2011 ) . Google Scholar
G. A. Leonov , N. V. Kuznetsov and V. I. Vagaitsev , Phys. Lett. A 375 , 2230 ( 2011 ) . Crossref, Web of Science, Google Scholar
G. A. Leonov , N. V. Kuznetsov and V. I. Vagaitsev , Physica D 241 , 1482 ( 2012 ) . Crossref, Web of Science, Google Scholar
G. A. Leonov and N. V. Kuznetsov , Int. J. Bifurcation and Chaos 23 , 1330002-1 ( 2013 ) . Link, Web of Science, Google Scholar
G. A. Leonov and N. V. Kuznetsov, Numerical Methods for Differential Equations, Optimization, and Technological Problems, Computational Methods in Applied Sciences 27 (Springer International Publishing, 2013) pp. 41–64. Crossref, Google Scholar
G. A. Leonov et al. , Nonlin. Dyn. 77 , 277 ( 2014 ) . Crossref, Web of Science, Google Scholar
M. Molaei et al. , Int. J. Bifurcation and Chaos 23 , 1350188-1 ( 2013 ) . Google Scholar
L. P. Shilnikov , Sov. Math. Dockl. 6 , 163 ( 1965 ) . Google Scholar
J. Sprott , Phys. Rev. E 50 , R647 ( 1994 ) . Crossref, Web of Science, Google Scholar
X. Wang and G. Chen , Nonlin. Dyn. 71 , 429 ( 2013 ) . Crossref, Web of Science, Google Scholar
Z. Wei , Phys. Lett. A 376 , 102 ( 2011 ) . Crossref, Web of Science, Google Scholar