Frequency locking near the gluing bifurcation: Spin-torque oscillator under periodic modulation of current

TL;DR

This paper analyzes how spin-torque oscillators near a homoclinic bifurcation respond to periodic forcing, revealing that such proximity complicates synchronization due to highly sensitive frequency behavior.

Contribution

It provides a general theoretical framework for understanding frequency locking near homoclinic bifurcations, with explicit expressions for resonance regions in spin-torque oscillators.

Findings

Proximity to homoclinic bifurcation impairs synchronization.

Explicit formulas for Arnold tongue borders are derived.

Frequency sensitivity increases near bifurcation points.

Abstract

We consider entrainment by periodic force of limit cycles which are close to the homoclinic bifurcation. Taking as a physical example the nanoscale spin-torque oscillator in the LC circuit, we develop the general description of the situation in which the frequency of the stable periodic orbit in the autonomous system is highly sensitive to minor variations of the parameter, and derive explicit expressions for the strongly deformed borders of the resonance regions (Arnold tongues) in the parameter space of the problem. It turns out that proximity to homoclinic bifurcations hinders synchronization of spin-torque oscillators.