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We present an analytical calculation of the response of a driven Duffing oscillator to low-frequency fluctuations in the resonance frequency and damping. We find that fluctuations in these parameters manifest themselves distinctively, allowing them to be distinguished. In the strongly nonlinear regime, amplitude and phase noise due to resonance frequency fluctuations and amplitude noise due to damping fluctuations are strongly attenuated, while the transduction of damping fluctuations into phase noise remains of order $1$. We show that this can be seen by comparing the relative strengths of the amplitude fluctuations to the fluctuations in the quadrature components, and suggest that this provides a means to determine the source of low-frequency noise in a driven Duffing oscillator.
Here we present a one-degree-of-freedom model of a nonlinear parametrically-driven resonator in the presence of a small added ac signal that has spectral responses similar to a frequency comb. The proposed nonlinear resonator has a spread spectrum re
Stochastic resonance (SR) is a coherence enhancement effect due to noise that occurs in periodically-driven nonlinear dynamical systems. A very broad range of physical and biological systems present this effect such as climate change, neurons, neural
Discrete fractional order chaotic systems extends the memory capability to capture the discrete nature of physical systems. In this research, the memristive discrete fractional order chaotic system is introduced. The dynamics of the system was studie
The phase reduction method for a limit cycle oscillator subjected to a strong amplitude-modulated high-frequency force is developed. An equation for the phase dynamics is derived by introducing a new, effective phase response curve. We show that if t
We describe the measurement of the secular motion of a levitated nanoparticle in a Paul trap with a CMOS camera. This simple method enables us to reach signal-to-noise ratios as good as 10$^{6}$ with a displacement sensitivity better than 10$^{-16},m