Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:D1L-B

Session:

Number:789

Bifurcation Structure of Augmented Lorenz Equations and Synchronizability of Coupled Augmented Lorenz Oscillators

Koki Yoshimito,  Kenichiro Cho,  Yuichiro Morita,  Takaya Miyano,  

pp.789-792

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.789

PDF download (1.2MB)

Summary:
The bifurcation structure of the augmented Lorenz equations as a starlike network of Lorenz subsystems is investigated as a function of the reduced Rayleigh number and the number of Lorenz subsystems by performing numerical simulations. Estimated bifurcation diagrams are discussed in relation to chaotic synchronization of directly coupled augmented oscillators with parameter mismatch.

References:

[1] S. H. Strogatz, Nonlinear Dynamics and Chaos (Addison-Wesley, Massachusetts, 1994) Chapter 9.

[2] M. Kolar and G. Gumbs, “Theory for the experimental observation of chaos in a rotating waterwheel,” Phys. Rev. A, vol.45, pp.626-637, 1992.

[3] E. N. Lorenz, “Deterministic non-periodic flow,” J. Atoms. Sci., vol.20, pp.130-141, 1963.

[4] K. Cho, Y. Okada, J. Tatsutani, T. Toriyama, T. Miyano, “Chaotic Gas Turbine Simulating the Motion of Convective Heat Flow,” Proc. 2011 Int. Symp. Nonlin. Theor. Appl. (NOLTA2011), pp.13-16, 2011.

[5] K. Cho, J. Tatsutani, T. Miyano, “Chaotic Synchronization of Augmented Lorenz Systems,” Proc. 2011 Int. Symp. Nonlin. Theor. Appl. (NOLTA2011), pp.476-479, 2011.

[6] T. Miyano, K. Cho, Y. Okada, J. Tatsutani, T. Toriyama, “Augmented Lorenz Equations as Physical Model for Chaotic Gas Turbine,” Procedia IUTAM, in print.

[7] K. Cho, T. Miyano, T. Toriyama, submitted.

[8] K. R. Sreenivasan, A. Bershadskii and J. J. Niemela, “Mean Wind and its Reversal in Thermal Convection,” Phys. Rev. E, vol.65, 056306, 2002.

[9] F. Fontenele Araujo, S. Grossmann and D. Lohse, “Wind Reversals in Turbulent Rayleigh-Bénard Convection,” Phys. Rev. Lett., vol.95, 084502, 2005.

[10] G. Ahlers, S. Grossmann and D. Lohse, “Heat transfer and large scale dynamics in turbulent Rayleigh-Benard convection,” Rev. Mod. Phys., vol.81, pp.503-537, 2009.

[11] A. H. Epstein and S. D. Senturia, “Macro Power from Micro Machinery,” Science, vol.276, p.1211, 1997.

[12] A. H. Epstein, “Millimeter-scale, Micro-Electro- Mechanical Systems Gas Turbine Engines,” ASME J. Eng. Gas Turbine Power, vol.126, pp.205-226, 2004.

[13] K. M. Cuomo and A. V. Oppenheim, “Circuit Implementation of Synchronized Chaos with Applications to Communications,” Phys. Rev. Lett., vol.71, no.1, pp.65-68, 1993.

[14] K. M. Cuomo, A. V. Oppenheim and S. H. Strogatz, “Synchronization of Lorenz-based chaotic circuits with applications to communications,” IEEE Trans. Circuits Syst. II, vol.40, pp.626-633, 1993.

[15] R. Barrio and S. Serrano, “A three-parametric study of the Lorenz model,” Physica D, vol.229, pp.43-51, 2007.

[16] R. Barrio and S. Serrano, “Bounds for the chaotic region in the Lorenz model,” Physica D, vol.238, pp.1615-1624, 2009.