Abstract
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".
Highlights
In mathematical modeling of oscillatory processes a mathematical model of a relatively simple dynamical system is often used to study the dynamics of much more complex systems. Typical example of this approach is the extensive use of pendulum models to study the dynamics of systems of an entirely different nature
In mathematical modeling of such systems, the limitation of excitation source power must be always taken into account
The aim of this work is to study the influence of various factors of delay on dynamical behaviour of these system
Summary
In mathematical modeling of oscillatory processes a mathematical model of a relatively simple dynamical system is often used to study the dynamics of much more complex systems. Pendulum mathematical models are widely used to describe the dynamics of various technical constructions, machines and mechanisms, in the study of cardiovascular system, financial markets, etc. In mathematical modeling of such systems, the limitation of excitation source power must be always taken into account Another important factor that significantly affects the change of steady-state regimes of dynamical systems, is the presence of different in their physical substance, factors of delay. In some cases, taking into account factors of delay leads only to minor quantitative changes in dynamical characteristics of pendulum systems. The study of the influence of the factors of delay on the dynamical stability of equilibrium positions of pendulum systems was initiated by Shvets and Mitropolsky – and his scientific school – in the 1980s [4]. The aim of this work is to study the influence of various factors of delay on dynamical behaviour of these system
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
