Appearance of chaos and hyperchaos in evolving pendulum network

TL;DR

This paper investigates how chaos and hyperchaos emerge in chains of coupled pendulums, revealing that dissipation, coupling strength, and ensemble size critically influence the onset and nature of chaotic dynamics.

Contribution

It provides a detailed analysis of the mechanisms leading to chaos and hyperchaos in pendulum networks, including the effects of dissipation, coupling, and ensemble size, with analytical and numerical validation.

Findings

Chaos arises through period doubling and tori destruction bifurcations.

Chaos can be induced or suppressed by adjusting dissipation and coupling.

Chaotic regimes are absent at sufficiently strong coupling.

Abstract

The study of deterministic chaos continues to be one of the important problems in the field of nonlinear dynamics. Interest in the study of chaos exists both in low-dimensional dynamical systems and in large ensembles of coupled oscillators. In this paper, we study the emergence of spatio-temporal chaos in chains of locally coupled identical pendulums with constant torque. The study of the scenarios of the emergence (disappearance) and properties of chaos is done as a result of changes in: (i) the individual properties of elements due to the influence of dissipation in this problem, and (ii) the properties of the entire ensemble under consideration, determined by the number of interacting elements and the strength of the connection between them. It is shown that an increase of dissipation in an ensemble with a fixed coupling force and elements number can lead to the appearance of chaos as a result of a cascade of period doubling bifurcations of periodic rotational motions or as a result of invariant tori destruction bifurcation. Chaos and hyperchaos can occur in an ensemble by adding or excluding one or more elements. Moreover, chaos arises hard, since in this case the control parameter is discrete. The influence of the coupling strength on the occurrence of chaos is specific. The appearance of chaos occurs with small and intermediate coupling and is caused by the overlap of the various out-of-phase rotational modes regions existence. The boundaries of these areas are determined analytically and confirmed in a numerical experiment. Chaotic regimes in the chain do not exist if the coupling strength is strong enough.