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Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion
Open accessAbstract
In this paper, we discuss self-excited and hidden attractors for systems of differential equations. We considered the example of a Lorenz-like system derived from the well-known Glukhovsky-Dolghansky and Rabinovich systems, to demonstrate the analysis of self-excited and hidden attractors and their characteristics. We applied the fishing principle to demonstrate the existence of a homoclinic orbit, proved the dissipativity and completeness of the system, and found absorbing and positively invariant sets. We have shown that this system has a self-excited attractor and a hidden attractor for certain parameters. The upper estimates of the Lyapunov dimension of self-excited and hidden attractors were obtained analytically.
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Cites
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Metadata
- Authors
- Leonov, G. A., Kuznetsov, N. V., & Mokaev, T. N.
- Venue
- The European Physical Journal Special Topics
- Published
- 2015-07
- Volume
- 224
- Issue
- 8
- Pages
- 1421-1458
- ISSN
- 1951-6355 (ISSN-L)
- 1951-6401
- OpenAlex
- W2127445253
- Cited by
- 386
- References
- 72
- FWCI
- 38.27
- Type
- journal article
- Language
- en
- Open access
- hybrid
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- Leonov, G. A., Kuznetsov, N. V., & Mokaev, T. N. (2015). Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion. The European Physical Journal Special Topics. https://doi.org/10.1140/epjst/e2015-02470-3
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