<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Dynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system is a system of ordinary differential equations with delay. Three approaches are suggested that allow to reduce the mathematical model of the system to systems of differential equations, into which various factors of delay enter as some parameters. Genesis of deterministic chaos is studied in detail. Maps of dynamic regimes, phase-portraits of attractors of systems, phase-parametric characteristics and Lyapunov characteristic exponents are constructed and analyzed. The scenarios of transition from steady-state regular regimes to chaotic ones are identified. It is shown, that in some cases the delay is the main reason of origination of chaos in the system "pendulum - source of limited excitation".</p></abstract>

Dynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system is a system of ordinary differential equations with delay. Three approaches are suggested that allow to reduce the mathematical model of the system to systems of differential equations, into which various factors of delay enter as some parameters. Genesis of deterministic chaos is studied in detail. Maps of dynamic regimes, phase-portraits of attractors of systems, phase-parametric characteristics and Lyapunov characteristic exponents are constructed and analyzed. The scenarios of transition from steady-state regular regimes to chaotic ones are identified. It is shown, that in some cases the delay is the main reason of origination of chaos in the system "pendulum - source of limited excitation".

Deterministic chaos in pendulum systems with delay

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"Deterministic chaos in pendulum systems with delay"}

Dynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system...

Deterministic chaos in pendulum systems with delay

Published Online: Feb 12, 2019

Page range: 1 - 8

Received: Nov 13, 2018

Accepted: Jan 12, 2019

DOI: https://doi.org/10.2478/AMNS.2019.1.00001

Keywords
chaotic attractor, system with limited excitation, factors of delay

© 2019 A. Shvets and A. Makaseyev, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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Deterministic chaos in pendulum systems with delay

Published Online: Feb 12, 2019

Page range: 1 - 8

Received: Nov 13, 2018

Accepted: Jan 12, 2019

DOI: https://doi.org/10.2478/AMNS.2019.1.00001

Keywordschaotic attractor, system with limited excitation, factors of delay

© 2019 A. Shvets and A. Makaseyev, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Keywords
chaotic attractor, system with limited excitation, factors of delay