Chaos-Geometric approach to analysis of chaotic attractor dynamics for the one-ring fibre laser
DOI:
https://doi.org/10.15673/2072-9812.1/2015.50224Parole chiave:
Geometry of chaos, Non-linear analysis, laser systemAbstract
Earlier we have developed new chaos-geometric approach to modelling and analysis of nonlinear processes dynamics of the complex systems. It combines together application of the advanced mutual information approach, correlation integral analysis, Lyapunov exponent's analysis etc. Here we present the results of its application to studying low-and high-D attractor dynamics of the one-ring fibre laserRiferimenti bibliografici
Glushkov A.V., Kuzakon' V.M., Khetselius O.Yu., Prepelitsa G.P. and Svinarenko A.A., Geometry of Chaos: Theoretical basis's of a consistent combined approach to treating chaotic dynamical systems and their parameters determination// Proc. Int. Geom. Centre.-2013.-Vol.6.-N1.-P6-12.
Glushkov A.V., Khetselius O.Yu., Florko T.A., Prepelitsa G.P., Chaos-Geometric approach to analysis of quantum-generator systems// Proc. Int. Geom. Centre.- 2014.-Vol.7,N4.-P.77-82.
Bunyakova Yu.Ya., Glushkov A.V.,Fedchuk A.P., Serbov N.G., Svinarenko A.A., Tsenenko I.A., Sensing non-linear chaotic features in dynamics of system of couled autogenerators: standard multifractal analysis// Sensor Electr. and Microsyst. Techn.-2007.-N1.-P.14-17.
Glushkov A.V., Khokhlov V.N., Loboda N.S., Bunyakova Yu.Ya., Short-range forecast of atmospheric pollutants using non-linear prediction method// Atmospheric Environment (Elsevier).-2008.-Vol.42.-P. 7284--7292.
Glushkov A.V., Svinarenko A.A., Buyadzhi V.V., Zaichko P.A., Ternovsky V.B., Chaos-geometric attractor and quantum neural networks approach to simulation chaotic evolutionary dynamics during perception process// Advances in Neural Networks, Fuzzy Systems and Artificial Intelligence, Series: Recent Advances in Computer Engineering (Gdansk,EU, World Sci.).-2014.-Vol.21.-P.143--150.
Glushkov A.V., Prepelitsa G.P., Lepikh Ya.I., Buyadzhi V.V., Ternovsky V.B., Zaichko P.A., Chaotic dynamics of non-linear processes in atomic and molecular systems in electromagnetic field and semiconductor and fiber laser devices: new approaches, uniformity and charm of chaos// Sensor Electronics and Microsystems Techn.-2014.-Vol.11,N4.-P.43--57.
Glushkov A.V., Khetselius O.Yu., Bunyakova Yu.Ya., Prepelitsa G.P., Solyanikova E.P., Serga E.N., Non-linear prediction method in short-range forecast of atmospheric pollutants: low-dimensional chaos// Dynamical Systems -- Theory and Applications. -- Lodz: Lodz Univ. Press (Poland). --2011.- LIF111 (6p.).
Glushkov A.V., Bunyakova Yu.Ya., Zaichko P.A., Geometry of Chaos: Consistent combined approach to treating chaotic dynamics atmospheric pollutants and its forecasting// Proc. of Int. Geometry Center.-2013.-Vol.6,N3.-P.6-14.
Feng C., Yu-Ling F., Zhi-Hai Y., Jian F., Yuan-Chao S., Yu-Zhu Z.: Experimental investigation on chaos generation in erbium-doped fiber single-ring lasers//Chin. Phys. B.-2013.-Vol. 21.-P.100504.
Kennel M., Brown R., Abarbanel H., Determining embedding dimension for phase-space reconstruction using a geometrical construction//Phys Rev A.-1992.-Vol.45.-P.3403--3411.
Packard N., Crutchfield J., Farmer J., Shaw R., Geometry from a time series//Phys Rev Lett.-1988.-Vol.45.-P.712--716.
Grassberger P., Procaccia I., Measuring the strangeness of strange attractors//Physica D.-1983.-Vol.9.-P.189--208.
Fraser A., Swinney H., Independent coordinates for strange attractors from mutual information// Phys Rev A.-1986.-Vol.33.-P.1134--1140.
Takens F (1981) Detecting strange attractors in turbulence. In: Rand DA, Young LS (eds) Dynamical systems and turbulence, Warwick 1980. (Lecture notes in mathematics No 898). Springer, Berlin Heidelberg New York, pp 366--381
Mane R (1981) On the dimensions of the compact invariant sets of certain non-linear maps. In: Rand DA, Young LS (eds) Dynamical systems and turbulence, Warwick 1980. (Lecture notes in mathematics No 898). Springer, Berlin Heidelberg N.-Y., p. 230--242
Sano M, Sawada Y (1985) Measurement of the Lyapunov spectrum from a chaotic time series//Phys Rev.Lett.-1995.-Vol.55.-P.1082--1085
