Features of the Behavior of Lyapunov’s Exponents Depending On Symmetry of Thermodynamic Potential, Described By the Lifshitz's Invariant

Electric Power Engineering & Control Systems

Authors

First and Last Name Academic degree E-mail Affiliation
Yurij Olenych No ivan.kuno [at] lnu.edu.ua Ivan Franko National University of Lviv
Lviv, Ukraine
Vasyl Kuno No incomlviv [at] gmail.com Ivan Franko National University of Lviv
Lviv, Ukraine
Sergiy Sveleba Sc.D. incomlviv [at] gmail.com Ivan Franko National University of Lviv
Lviv, Ukraine
Ivan Katerynchuk Ph.D. Incomlviv [at] gmail.com Ivan Franko National University of Lviv
Lviv, Ukraine
Ivan Kuno Ph.D. ivan_kunyo [at] yahoo.com Ivan Franko National University of Lviv
Lviv, Ukraine
ivan Karpa Ph.D. incomlviv [at] gmail.com Ivan Franko National University of Lviv
Lviv, Ukraine

I and my co-authors (if any) authorize the use of the Paper in accordance with the Creative Commons CC BY license

First published on this website: 16.09.2019 - 22:49
Abstract

Characteristic Lyapunov’s exponents allow to conduct qualitative analysis of dynamic systems. As is known, the Lyapunov’s exponents of a dynamical system is a value that characterizes the rate of separation of infinitely close trajectories. It plays a decisive role in the discovery of dynamic behavior and the chaotic degree of a strange attractor. Therefore, the purpose of this work is to calculate Lyapunov indices for a incommensurate superstructure. The Lyapunov coefficients were calculated in Python using Skipy, JiTCODE libraries.

References

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[3]     Ktitorov S. A., Pogorelov Ph. A., Charnaya E. V. (2009). Inhomogeneous configurations in the Lifshitz-type improper incommensurate ferroelectric thin films. Physics of the Solid State, 51 (8), 1570–1573.

[4]     Cummins H. Z. (1990). Experimental Studies of structurally incommensurate crystal phases  Physics Reports, 185 (5), 211–409.

[5]     Sveleba S., Katerynchuk I., Kunyo I., Karpa I. (2018). Properties of Anisotropic Interaction of the Incommensurate Superstructure as Described by Dziloshinsky’s Invariant. The X th International Scientific and Practical Conference "Electronics and Information Technologies" (ELIT-2018). A-159–162.

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Myroslav Sabat
Myroslav Sabat's picture
reviewer, secretary

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Fri, 10/18/2019 - 10:22