Delay as an energy regulator of the generation of deterministic chaos in hydrodynamic systems with limited excitation

TL;DR

This paper investigates how delay in excitation influences the emergence and suppression of deterministic chaos in hydrodynamic systems, revealing that delay can qualitatively alter system attractors and transition scenarios.

Contribution

It introduces a novel technique for analyzing attractors in delayed hydrodynamic systems and demonstrates the critical role of delay in chaos regulation.

Findings

Delay causes qualitative changes in attractors.

Regular attractors can become chaotic with delay.

Delay variations lead to different transition scenarios.

Abstract

The Miles-Krasnopolskaya system is considered, which is used to study the nonlinear interaction of a tank with a liquid and the source of excitation of its oscillations. Additionally, delay time of impulse from the source of excitation of oscillations on the dynamics of the aggregate system "tank with liquid - source of excitation" is taken into account. A technique for studying the attractors of such systems is proposed. It is shown that delay plays a key role in the emergence (disappearance) of deterministic chaos in the Miles-Krasnopolskaya system. Quantitative changes in the value of the delay can lead to qualitative changes in the types of attractors of the system. So, regular attractors can turn into chaotic ones and vice versa. Also, a change in the delay value can lead to the implementation of new scenarios, both transitions from regular attractors to chaotic ones and transitions from a chaotic attractor of one type to a chaotic attractor of another type.