• E. V. Pavlov Одеський національний університет імені І. І. Мечникова
  • A. V. Ignatenko Odessa State Environmental University
  • S. V. Kirianov Odessa State Environmental University
  • A. A. Mashkantsev Odessa State Environmental University



Ключові слова:

Chaotic dynamics, diatomic molecule, electromagnetic field


Nonlinear chaotic dynamics of the PbO molecule interacting with a resonant linearly polarized electromagnetic field is computed within the quantum model, based on the numerical solution of the Schrödinger equation and model potential method. To calculate the system dynamics in a chaotic regime the known chaos theory and non-linear analysis methods such as a correlation integral algorithm, the Lyapunov’s exponents and  Kolmogorov entropy analysis are used. There are listed the data of computing dynamical and topological invariants such as the correlation, embedding and Kaplan-Yorke dimensions, Lyapunov’s exponents, Kolmogorov entropy etc..


Zhang C.; Katsouleas T.; Joshi C. Harmonic frequency generation & chaos in laser driven molecular vibrations. In Proc. of Short-wavelength Physics with Intense Laser Pulses, San-Diego. 1993.

Berman, G.; Bulgakov, E.; Holm, D. Nonlinear resonance and dynamical chaos in diatomic molecule driven by a resonant IR field. Phys. Rev. A 1995, 52, 3074

López, G.; Mercado, A. classical chaos on double nonlinear resonances in diatomic molecules. J. Mod. Phys. 2015, 6, 496-509.

Glushkov, A.V. Spectroscopy of atom and nucleus in a strong laser field: Stark effect and multiphoton resonances. J. Phys.: Conf. Ser. 2014, 548, 012020.

Ignatenko A., Buyadzhi A., Buyadzhi V., Kuznetsova, A.A., Mashkantsev, A.A., Ternovsky E. Nonlinear chaotic dynamics of quantum systems: molecules in an electromagnetic field. Adv. Quant Chem. 2019, 78, 149-170.

Glushkov, A., Buyadzhi, V., Kvasikova, A., Ignatenko, A., Kuznetsova, A., Prepelitsa, G., Ternovsky, V. Non-Linear chaotic dynamics of quantum systems: Molecules in an electromagnetic field and laser systems. In: Quantum Systems in Physics, Chemistry, and Biology. Springer, Cham. 2017, 30, 169-180

Mashkantsev, A. A. ; Ignatenko, A.V. ; Kirianov, S.V. ; Pavlov, E.V. Chaotic dynamics of diatomic molecules in an electromagneic field. Photoelectronics. 2018, 27, 103-112.

Glushkov A., Ternovsky V., Buyadzhi V, Prepelitsa G. Geometry of a relativistic quantum chaos: New approach to dynamics of quantum systems in electromagnetic field and uniformity and charm of a chaos. Proc. Int. Geom. Center. 2014, 7(4), 60-71.

Glushkov A.V.; Ivanov, L.N. DC strong-field Stark effect: consistent quantum-mechanical approach. J. Phys. B: At. Mol. Opt. Phys. 1993, 26, L379-386.

Glushkov, A.; Lovett, L.; Khetselius, O.; Gurnitskaya E.; Dubrovskaya, Y.; Loboda A. Generalized multiconfiguration model of decay of multipole giant resonances applied to analysis of reaction (μ - n) on the nucleus 40Ca. Int. J. Mod. Phys. A. 2009, 24(2-3), 611-615.

Serbov N., Svinarenko A. Wavelet and multifractal analysis of oscillations in system of couled autogenerators in chaotic regime. Photoelectr. 2006, 15, 27.

Serbov, N., Svinarenko, A. Wavelet and multifractal analysis of oscillations in a grid of couled autogenerators. Photoelectr. 2007, 16, 53-56.

Glushkov, A.V.; Khetselius, O.Yu.; Svinarenko, A.A.; Serbov, N.G. The sea and ocean 3D acoustic waveguide: rays dynamics and chaos phenomena, J. Acoust. Soc. Amer. 2008, 123(5), 3625.

Glushkov A.V., Serbov N.G., Bunyakova Yu.Ya., Prepelitsa G.P., Svinarenko A.A. Sensing the kinetical features of energy exchange in mixture CO2-N2-H20 of atmospheric gases under interacting with laser radiation. Sensor Electr. and Microsyst. Techn. 2006. N4. P.20-22.

Danilov, V., Kruglyak, Y., Pechenaya, V. Electron density-bond order matrix and the spin density in the restricted CI method. Theor. Chim Acta. 1969, 13(4), 288-296.

Danilov, V., Kruglyak, Y., Kuprievich, V., Ogloblin, V. Electronic aspects of photodimerization of the pyrimidine bases and of their derivatives. Theor. Chim.Acta. 1969, 14(3), 242-249.

Abarbanel, H.; Brown, R.; Sidorowich, J; Tsimring, L. The analysis of observed chaotic data in physical systems. Rev. Mod. Phys. 1993, 65, 1331- 1392.

Kennel, M.; Brown, R.; Abarbanel, H. Determining embedding dimension for phase-space reconstruction using geometrical construction. Phys. Rev. A. 1992, 45, 3403-3412.

Glushkov, A.V. Methods of a Chaos Theory. Astroprint: Odessa, 2012.

Khetselius, O. Forecasting evolutionary dynamics of chaotic systems using advanced non-linear prediction method In Dynamical Systems Applications; Łódz, 2013; Vol T2, pp 145-152.

Glushkov A., Khetselius O., Bunyakova Yu., Prepelitsa G., Solyanikova E., Serga E. Non-linear prediction method in short-range forecast of atmospheric pollutants: low-dimensional chaos. In: Dynamical Systems - Theory and Applications. Lodz Univ. 2011, LIF111

Glushkov A., Khetselius O., Kuzakon V., Prepelitsa G., Solyanikova E., Svinarenko A. Modeling of interaction of the non-linear vibrational systems on the basis of temporal series analyses (application to semiconductor quantum generators). Dynamical Systems - Theory and Applications. Lodz. 2011, BIF110.

Glushkov, A.., Safranov, T., Khetselius, O., Ignatenko, A., Buyadzhi, V., Svinarenko, A. Analysis and forecast of the environmental radioactivity dynamics based on methods of chaos theory: General conceptions. Environm. Probl.. 2016, 1(2), 115-120.

Glushkov, A., Khetselius, O., Serbov, N., Svinarenko, A., Buyadzhi, V. Dynamics of multi-layers neural networks on bais of photon echo: Effects of chaos and stochastic resonance. Proc. of Int.. Conf. on Statistical Phys. Crete. 2008, 26

Bunyakova Yu.; Glushkov, A.; Fedchuk A; Serbov N.; Svinarenko A.; Tsenenko, I. Sensing non-linear chaotic features in dynamics of system of coupled auto generators: multifractal analysis, Sensor Electr.& Microsyst. Techn. 2007, 1,14-17

Glushkov, A.V.; Buyadzhi, V.V.; Ponomarenko, E.L. Geometry of Chaos: Advanced approach to treating chaotic dynamics in some nature systems. Proc. Int. Geom. Center. 2014 7(1),24-30.

Oolg, M.; Nicklass, A.; Stoll, H. On the dipole moment of PbO. J. Chem. Phys. 1993, 99 (5), 3614.