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Charts of the Lyapunov exponents for the four dissipatively coupled phase **oscillators** on the **frequency** detunings parameter plane (Δ1,Δ3). Values of the parameters are μ=0.4, (а) Δ2=0.4, (b) Δ2=2.4. Resonance conditions in the chain of **oscillators** are shown by arrows.
... Examples of phase portraits for the system (2). (a) Two-**frequency** resonance regime of the type 1:3 for Δ1=−1.5, Δ2=1, μ=0.6; (b) three-**frequency** regime for Δ1=−1, Δ2=1, μ=0.25.
... Chart of the Lyapunov exponents for three coupled van der Pol **oscillators** on the **frequency** detunings parameter plane. Numbers correspond to cycle periods in the Poincaré section. Values of the parameters are λ=0.1,μ=0.04.
... Chart of the Lyapunov exponents for three coupled van der Pol **oscillators** on the **frequency** detunings parameter plane. Numbers correspond to cycle periods in the Poincaré section. Values of the parameters are λ=1,μ=0.4.
... Chain of van der Pol **oscillators**... Full synchronization area for the four phase **oscillators** on the **frequency** detunings parameter space (Δ1,Δ2,Δ3).

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We consider the interaction between a single cavity mode and N≫1 identical **qubits**, assuming that any system parameter can be rapidly modulated in situ by external bias. It is shown that, for the **qubits** initially in the ground states, three photons can be coherently annihilated in the dispersive regime for harmonic modulation with **frequency** 3ω0−Ω0, where ω0 (Ω0) is the bare cavity (**qubit**) **frequency**. This phenomenon can be called “Anti-dynamical Casimir effect”, since a pair of excitations is destroyed without dissipation due to the external modulation. For the initial vacuum cavity state, three **qubit** excitations can also be annihilated for the modulation **frequency** 3Ω0−ω0.

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The plots of 1H signal width for the crystalline region of polyethylene thin film on the surface of on an piezoelectric **oscillator** plate against **oscillation** **frequency** in the range from 1 Hz to 2 MHz (a) and in the expanded range from 1 Hz to 100 kHz (b) at 40 °C.
... The plots of 1H signal width for the non-crystalline region of polyethylene thin film on the surface of on a piezoelectric **oscillator** plate against **oscillation** **frequency** in the range from 1 Hz to 2 MHz (a) in the expanded range from 1 Hz to 100 kHz (b) at 40 °C.
... A diagram of an NMR glass tube with an piezoelectric **oscillator** plate. The polyethylene thin film was molten and adhered on the surface of piezoelectric **oscillator** plate. The **oscillation** of an piezoelectric **oscillator** plate is generated by AD alternator.

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Measured and simulated output power spectrum for the **oscillators** at Vg=0V and Vc=1.0V (left). The fundamental **oscillation** is at 15.71GHz. The bias stability diagram of the **oscillator** (right).
... Measured **oscillation** **frequency** as a function of gate bias at Vc=2.4V. The arrows indicate the two sweep directions.
... Measured **oscillator** output power for varying DC gate biases. The squares represent the fundamental **oscillation** **frequency**, the circles the 2nd harmonic and the stars the 3rd harmonic **oscillation**.
... Measured performance operating the **oscillator** as a mixer.
... Measured (circles) and simulated (squares) **oscillation** **frequencies** for different wave-guides specified in Table 1. The data points for D are solid while C are open.

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Theory and simulation results of the normalized digital **frequency** fD as a function of the f0/fS ratio and ρ=0.01. The r and δ values which identify each f0/fS segment are also specified.
... Oscilloscope screen captures of resonator position, input pulses (D6), delayed comparator output (D3) and sample clock (D0), for a PDO topology with m=1 and a ‘not perfect’ **frequency** fS=46.093kHz (r=2).
... Pulsed digital **oscillators**, MEMS, **Oscillators**, Sigma-delta... Oscilloscope screen captures of resonator position, input pulses (D6), delayed comparator output (D3 and D1) and sample clock (D0), for a PDO topology with m=2 and the ‘perfect’ **frequency** fS=44.052kHz (r=2).

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The output **frequency** response of a nonlinear system.
... The restoring force of a bilinear **oscillator**.
... The output **frequency** response of a linear system.
... Bilinear **oscillator**... The polynomial approximation result for a bilinear **oscillator**
... Nonlinear output **frequency** response function... Bilinear **oscillator** model.

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Dominant **frequency**... The first and the second dominant **frequencies** variation with the steam mass flux.
... The first and the second dominant **frequencies** variation with the water temperature.
... The dominant **frequency** regime map.
... Pressure **oscillation**... **Frequency** spectrums of pressure **oscillation** at different water temperatures and steam mass flux.
... The dominant **frequencies** in different measurement points by Qiu et al. [14].

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