Abstract
Numerical methods are used to study a spatially distributed system of two nonlinear stochastic equations that simulate interacting phase transitions. Conditions for self-oscillations and waves are determined. The 1/f and 1/k spectra of extreme fluctuations are formed when waves emerge and move under the action of white noise. The distribution of the extreme fluctuations corresponds to the maximum entropy, which is proven by the stability of the 1/f and 1/k spectra. The formation and motion of waves under external periodic perturbation are accompanied by spatiotemporal chaotic resonance in which the domain of periodic pulsations is extended under the action of white noise.
Similar content being viewed by others
References
P. Bak, How Nature Works (Springer, Berlin, 1996).
B. Mandelbrot, The Fractal Geometry of Nature (W. H. Freeman, New York, 1982).
Yu. L. Klimontivich, Statistical Theory of Open Systems (Kluwer, Dordrecht, 1995).
F. Corberi, J. Phys. A 48, 465003 (2015).
V. N. Skokov, V. P. Koverda, and A. V. Reshetnikov, JETP Lett. 69, 636 (1999).
V. N. Skokov, V. H. Koverda, A. V. Reshetnikov, V. P. Skripov, N. A. Mazheiko, and A. V. Vinogradov, Int. J. Heat Mass Transfer 46, 1879 (2003).
V. N. Skokov, V. P. Koverda, A. V. Reshetnikov, and A. V. Vinogradov, Phys. A 364, 63 (2006).
A. N. Kolmogorov, Dokl. Akad. Nauk SSSR 30, 299 (1941).
P. Bak, C. Tang, and K. Wiesenfeld, Phys. Rev. A 38, 364 (1988).
B. B. Mandelbrot and J. W. Van Ness, SIAM Rev. 10, 422 (1968).
V. P. Koverda, V. N. Skokov, and V. P. Skripov, J. Exp. Theor. Phys. 86, 953 (1998).
V. P. Koverda and V. N. Skokov, Phys. A 262, 376 (1999).
V. P. Koverda and V. N. Skokov, Dokl. Phys. 55, 483 (2010).
V. P. Koverda and V. N. Skokov, Phys. A 391, 21 (2012).
V. S. Anishchenko, A. B. Neiman, F. Moss, and L. Shimansky-Geier, Phys.-Usp. 42, 7 (1999).
V. N. Skokov and V. P. Koverda, Tech. Phys. 59, 637 (2014).
V. P. Koverda and V. N. Skokov, Phys. A 393, 173 (2014).
V. P. Koverda and V. N. Skokov, Dokl. Phys. 58, 433 (2013).
V. P. Koverda and V. N. Skokov, Dokl. Phys. 47, 654 (2002).
A. G. Bashkirov, Theor. Math. Phys. 149, 1559 (2006).
V. P. Koverda and V. N. Skokov, Tech. Phys. 55, 442 (2010).
V. P. Koverda and V. N. Skokov, Tech. Phys. 61, 1135 (2016).
V. P. Koverda and V. N. Skokov, Dokl. Phys. 61, 535 (2016).
E. W. Montroll and M. F. Shlesinger, J. Stat. Phys. 32, 209 (1983).
C. Tsallis, J. Stat. Phys. 52, 479 (1988).
A. Renyi, Probability Theory (North-Holland, Amsterdam, 1970).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.P. Koverda, V.N. Skokov, 2018, published in Zhurnal Tekhnicheskoi Fiziki, 2018, Vol. 88, No. 5, pp. 655–662.
Rights and permissions
About this article
Cite this article
Koverda, V.P., Skokov, V.N. Oscillations and Waves in a Nonlinear System with the 1/f Spectrum. Tech. Phys. 63, 634–640 (2018). https://doi.org/10.1134/S1063784218050134
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S1063784218050134