Delay factors in the genesis of limit sets of the non-ideal system "tank with liquid-electric motor"
I. A. Seit-Dzhelil, A. Yu. Shvets
TL;DR
The paper examines how delays $\delta$ and $\rho$ in a non-ideal tank with a liquid-electric motor influence the genesis and evolution of attractors, ranging from limit cycles to invariant tori, chaotic, and hyperchaotic states. It develops two delay-approximation schemes to convert the inherently infinite-dimensional delay system into finite-dimensional ODEs, enabling detailed Lyapunov and bifurcation analyses. Key findings include a progression from simple periodic dynamics to complex toral and chaotic regimes, with transitions governed by specific bifurcations such as Neimark-Sacker and period-doubling, and the emergence of generalized intermittency leading to hyperchaos. The results underscore the necessity of accurate delay modeling for large delays and have implications for understanding and controlling fluid–electromechanical systems with delayed feedback.
Abstract
Non-ideal deterministic system "tank with liquid-electric motor" is studied. Two delay-approximation models are considered. Impact of the delay on the emergence, evolution and disappearance of regular and chaotic limit sets (attractors) of the system is investigated. The main dynamic characteristics of the system's steady-state regimes are computed and analyzed. Transition to chaos scenarios are studied. Realization of generalized intermittency scenario driven by delay factors is established.