Synchronization and anchoring of two non-harmonic canonical-dissipative oscillators via Smorodinsky-Winternitz potentials

TL;DR

This paper investigates how two non-harmonic oscillators with Smorodinsky-Winternitz potentials naturally synchronize through dissipative coupling, analyzing phase differences and synchronization quality.

Contribution

It demonstrates that canonical-dissipative modeling inherently induces coupling leading to synchronization in non-harmonic oscillators with detailed analysis.

Findings

Coupling force naturally arises from the dissipative framework.

Synchronization occurs with specific phase differences.

Degree of synchronization depends on system parameters.

Abstract

Two non-harmonic canonical-dissipative limit cycle oscillators are considered that oscillate in one-dimensional Smorodinsky-Winternitz potentials. It is shown that the standard approach of the canonical-dissipative framework to introduce dissipative forces leads naturally to a coupling force between the oscillators that establishes synchronization. The non-harmonic character of the limit cycles in the context of anchoring, the phase difference between the synchronized oscillators, and the degree of synchronization are studied in detail.