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Generic behavior of master-stability functions in coupled nonlinear dynamical systems
Abstract
Master-stability functions (MSFs) are fundamental to the study of synchronization in complex dynamical systems. For example, for a coupled oscillator network, a necessary condition for synchronization to occur is that the MSF at the corresponding normalized coupling parameters be negative. To understand the typical behaviors of the MSF for various chaotic oscillators is key to predicting the collective dynamics of a network of these oscillators. We address this issue by examining, systematically, MSFs for known chaotic oscillators. Our computations and analysis indicate that it is generic for MSFs being negative in a finite interval of a normalized coupling parameter. A general scheme is proposed to classify the typical behaviors of MSFs into four categories. These results are verified by direct simulations of synchronous dynamics on networks of actual coupled oscillators.
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Cites
The chemical basis of morphogenesis
Turing, A. M. (1952) · Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences · doi:10.1098/rstb.1952.0012 · Cited by 11,733
CHEN, G., & UETA, T. (1999) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127499001024 · Cited by 2,838
Cited by
Explosive transitions in complex networks’ structure and dynamics: Percolation and synchronization
Boccaletti, S., Almendral, J. A., Guan, S., Leyva, I., Liu, Z., Sendiña-Nadal, I., Wang, Z., & Zou, Y. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.10.004 · Cited by 363
Synchronization of chaotic systems: a microscopic description
Lahav, N., Sendiña-Nadal, I., Hens, C., Ksherim, B., Barzel, B., Cohen, R., & Boccaletti, S. (2018) · Physical Review E · doi:10.1103/physreve.98.052204 · Cited by 17
Metadata
- Authors
- Huang, L., Chen, Q., Lai, Y.-C., & Pecora, L. M.
- Venue
- Physical Review E
- Publisher
- American Physical Society (APS)
- Published
- 2009-09-15
- Volume
- 80
- Issue
- 3
- Pages
- 036204-036204
- ISSN
- 1539-3755 (ISSN-L)
- 1550-2376
- OpenAlex
- W2060305991
- Cited by
- 310
- References
- 2
- FWCI
- 13.94
- Type
- journal article
- Language
- en
- Open access
- closed
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- Huang, L., Chen, Q., Lai, Y.-C., & Pecora, L. M. (2009). Generic behavior of master-stability functions in coupled nonlinear dynamical systems. Physical Review E. https://doi.org/10.1103/physreve.80.036204
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