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

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### 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.

### Most cited references6

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### Oscillatory transient regime in the forced dynamics of a spin torque nano-oscillator

(2009)
We demonstrate that the transient non-autonomous dynamics of a spin torque nano-oscillator (STNO) under a radio-frequency (rf) driving signal is qualitatively different from the dynamics described by the Adler model. If the external rf current $$I_{rf}$$ is larger than a certain critical value $$I_{cr}$$ (determined by the STNO bias current and damping) strong oscillations of the STNO power and phase develop in the transient regime. The frequency of these oscillations increases with $$I_{rf}$$ as $$\propto\sqrt{I_{rf} - I_{cr}}$$ and can reach several GHz, whereas the damping rate of the oscillations is almost independent of $$I_{rf}$$. This oscillatory transient dynamics is caused by the strong STNO nonlinearity and should be taken into account in most STNO rf applications.
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### The gluing bifurcation: I. Symbolic dynamics of closed curves

(1988)
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### Multiple synchronization attractors of serially connected spin-torque nanooscillators

(2012)
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### Author and article information

###### Journal
1511.05827

Nonlinear & Complex systems