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".

New models and properties of forced oscillations of the various physical systems (pendulum and piezoceramic transducer) due to the interaction with the excitation device of limited power-supply are investigated in details. Using an analysis of the largest Lyapunov exponent for a complicated system-vibrating subsystem and exciter-the regions for three steady state regimes are determined, namely: stationary, periodic and chaotic.

No abstract

No abstract

No abstract