期刊
EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS
卷 224, 期 8, 页码 1421-1458出版社
SPRINGER HEIDELBERG
DOI: 10.1140/epjst/e2015-02470-3
关键词
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资金
- Russian Scientific Foundation [14-21-00041]
- Saint-Petersburg State University
- Russian Science Foundation [14-21-00041] Funding Source: Russian Science Foundation
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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