Contributors:V.K. Chandrasekar, Jane H. Sheeba, R. Gladwin Pradeep, R.S. Divyasree, M. Lakshmanan
Projected phase space of system (30) in the x1–x3 plane with N=10, for two different values q=3 ((a), (c)) and q=5 ((b), (d)), respectively. (a) and (b) describe the 2:1 period oscillations for the choice ω1=2 and ω2,ω3,…,ω10=1. (c) and (d) describe the quasiperiodic oscillations for the choice ω1=2 and ω2,ω3,…,ω10=1.
... (a) Time series plot of Eq. (15) for q=3 exhibiting periodic oscillations with the initial condition x(0)=3 and x˙(0)=0 for ω=1. (b) Phase space portrait of Eq. (15).
... Projected phase space of the almost integrable system (51) in the x1–x2 plane for the choices (a) ω1=1, ω2=2 exhibiting 1:2 period oscillation, (b) ω1=2, ω2=1 exhibiting quasiperiodic oscillation.
... Nonlinear oscillators... (Color online.) (a) Time series plot of Eq. (1) exhibiting periodic oscillation for three different initial conditions (three different colors) and ω=1.0. (b) Phase space portrait of Eq. (1).
Pressure fluctuations in the 8-in. burner for the stable combustion case ((A), Φ=0.7) and for the oscillating case ((B), Φ=1.0) under the fixed air flow rate condition Qa=800m3/h.
... Pressure fluctuations spectra of the 12-in. burner for the stable combustion case ((A), part (a) of Fig. 11A), and for the oscillating case ((B), part (a) of Fig. 11B), and for the early stage of the high frequencyoscillation ((C), part (b) of Fig. 11B).
... Pressure fluctuations spectra of the 8-in. burner for the stable combustion case ((A), part (a) of Fig. 8A), and for the oscillating case ((B), part (a) of Fig. 8B), and for the early stage of the high frequencyoscillation ((C), part (b) of Fig. 8B).
... Natural frequencies of tangential/radial mode oscillations of the 12-in. burner (A) and the experimental peak frequencies (B) (peak frequencies (c)–(h) in Fig 12B).
... Natural frequencies of tangential/radial mode oscillations of the 8-in. burner (A) and the experimental peak frequencies (B) (peak frequencies (c)–(h) in Fig 10B).
Van der Pol oscillator (18) for a=1,q=1,r=0,ω0=1,s=0.5,x0=0,x˙0=1.
... Ueda oscillator; Eq. (1) for p=0.05,q=0,r=1,s=7.5,ω0=1,x0=0,x˙0=1.
... Van der Pol oscillator (18) for a=0.05,q=1,r=1,ω0=0.38,s=0.16,x0=0,x˙0=-1.
An example of multiple oscillations present simultaneously (industrial tag 20).
... Oscillation analysis of pilot plant tags: (a) low frequency (b) high frequency.
... Oscillation analysis for pilot plant tags
... Oscillation analysis for industrial data
... Oscillations detected in the industrial data set. Open symbols are spurious oscillations lying on filter boundaries.
Entrainment of spontaneous oscillation by an external stimulus. (A) Sinusoidal forces were applied to a spontaneously oscillating hair cell bundle for three different stimulation conditions: one at the frequency of the spontaneous oscillations (FO=4kHz) and two for slightly lower frequency (3.5kHz). Thick lines are bundle tip displacements and thin red lines are external stimuli. Initial states of the bundle for the three simulations were the same and selected to have the opposite phase to the stimulus. (B) Bundle displacement in response to the three different stimuli in (A) averaged over 160 presentations (top two records) and 80 presentations (bottom record). Note that the response at FO (4kHz, top) builds up with a time constant of 0.7ms, indicative of a sharply tuned resonator. The bundle entrained poorly to the 3.5kHz stimulus at low level (middle), but at the higher level the force was sufficient to suppress the spontaneous movement and the bundle movement was entrained to the external stimulus. (C) A single cycle of bundle displacement (red line) averaged over 200ms of response compared to the force stimulus (black line), which was scaled for comparison with displacements. The bundle compliance obtained by dividing the displacement amplitude by the force amplitude is given beside each trace. (D) PSD plots for each response showing a sharply tuned response at FO (top). At 3.5kHz, the spectral density contains frequency components (both the spontaneous oscillation and the stimulus; middle). For the larger stimulus level at 3.5kHz, the spectral density is now dominated by the stimulus frequency.
... Effects of Ca2+ on the spontaneous oscillation. Different levels of the calcium concentration at the fast adaptation site were simulated. The bundle oscillated when the Ca2+ concentration at the fast adaptation site was between 12 and 30μM. Other parameters were identical to those given in Table 1. The hair bundle oscillated most strongly at 4kHz with Ca2+ of 20μM. The oscillationfrequency increased from 3kHz to 4.5kHz as the Ca2+ concentration increased from 12 to 30μM. Note the “twitch-like” behavior at low Ca2+.
... Compressive nonlinearity demonstrated by entrainment to an external stimulus. The hair cell bundle was stimulated with sinusoidal forces with different frequencies (1–16kHz) and magnitudes (0.1–1000 pN). (A) Representative examples of average bundle tip displacements (solid lines) and force stimuli (broken lines) scaled for comparison with displacements for one stimulus cycle. Displacements were averaged cycle by cycle over 200ms of response. (B) Bundle displacement plotted against stimulation frequency for three different force magnitudes. Note the sharp tuning for small 1 pN stimuli and the broad tuning for the largest 100 pN stimuli. (C) Bundle displacement plotted against force magnitude at the frequency of the spontaneous oscillations, FO=4kHz. Note that the relationship displays a compressive nonlinearity for intermediate stimulus levels, is linear at low stimulus levels, and again approaches linearity (denoted by dashed line) at the highest levels. (D) Gain plotted against stimulation frequency for three different force magnitudes. Gain is defined as the ratio of the compliance under the stimulus conditions to the passive compliance with the MT channel blocked. (E) Gain plotted against force magnitude at the frequency of the spontaneous oscillations, FO=4kHz. The gain declines from a maximum of 50 at the lowest levels, approaching 1 (passive) at the highest levels.
... Determinant of frequency: KD, Ca2+ dissociation constant. (A) The hair bundle morphology of a rat high-frequency hair cell was used to create a new FE model. The hair bundle had more stereocilia of smaller maximum height, (2.4μm compared to 4.2μm) than the low-frequency bundle. (B) Spontaneous oscillations of bundle position and open probability. (C) PSD plots indicating sharply tuned oscillations at 23kHz. For these simulations, KD and CFA, the Ca2+ concentration near the open channel, were elevated five times. Other values as in Table 1 except: fCa=8 pN and f0, the intrinsic force difference between open and closed states=−15 pN.
... Effects of loading the hair bundle with a tectorial membrane mass. (A) Passive resonance of a low-frequency (solid circles) and a high-frequency (open circles) hair bundle in the absence of the tectorial membrane mass with MT channels blocked. The system behaves as a low-pass filter with corner frequency of 23kHz (solid circles) and 88kHz (open circles). The hair bundle was driven with a sinusoidal force stimulus of 100 pN amplitude at different frequencies. (B) Passive behavior of the same two hair bundles surmounted by a block of tectorial membrane. The block of tectorial membrane had a mass of 6.2×10−12 kg for the low-frequency location, which was decreased fourfold for the high-frequency location. The MT channels were blocked, so the system was not spontaneously active. Resonant frequencies: 5.1kHz (solid circles) and 21kHz (open circles). (C). The active hair bundles, incorporating MT channel gating, combined with the tectorial membrane mass generated narrow-band spontaneous oscillations. PSD function is plotted against frequency, giving FO=2.9kHz, Q=40 for the low-frequency location, and FO=14kHz, Q =110 for the high-frequency location.
Contributors:M. Panagopoulou, C. Psychalinos, F.A. Khanday, N.A. Shah
Sinh-Domain lossy integrator with independent electronic adjustment of the cutoff frequency and gain.
... Output waveforms for the six-phase Sinh-Domain oscillator.
... Demonstration of the electronic tunability of the oscillator in Fig. 6.
... Sinusoidal oscillators... Multiphase oscillators
Amplitude spectra of our entire data sets for HD 101065 acquired on HJD 2456460 – 6462. Panel (a) clearly shows the principal frequency of oscillation ν1=1.372867 mHz, and the secondary frequency ν2=0.954261 mHz. On pre-whitening ν1, we are left with ν2 in panel (b). Panel (c) gives the residuals after pre-whitening ν2. There is still evidence of further frequencies although below the detection criterion.
... Amplitude spectra of HD 101065 data acquired on HJD 2456460 – 6462. Panel (a) clearly shows the principal frequency of oscillation ν1=1.372867 mHz, and the secondary frequency ν2=0.954261 mHz. On pre-whitening ν1, we are left with ν2 in panel (b). Again, on pre-whitening ν2, we are left with low frequency residuals peaks in panel (c) which still suggests possible presence of further oscillationfrequencies.
... The Non-linear least-square fit for the principal frequency ν1=1.372865 mHz. The JohnsonB amplitude of oscillation from year 1978 – 1988 were adopted from Martinez and Kurtz (1990), while that of year 2013 represent the amplitude and phase of oscillation secured from our combined data set (HJD 2456404 – 6462). Apart from year 2013 observation which has been analysed using 40-s integrations, 80-s integrations were used in all earlier observations adopted from Martinez and Kurtz (1990)).
... Stars: oscillations... The corresponding nightly amplitude spectra of HD 101065 on HJD 2456404 – 6462. Note the presence of resolved secondary frequencies ν2 in each panel around the region of 1 mHz. The known principal oscillationfrequency ν1 is also present in all the panels, while 2ν1 which is the harmonic of ν1 appears marginally in panel (b) only.
... Non-linear least-square fit for the frequencies secured from our combined data set (HJD 2456404 – 6462).
Oscillator... Measured temperature dependence of the oscillator's amplitude with constant driving frequency and amplitude at the beginning of the plateau.
... Simulated frequency response of the mechanically controlled oscillator. Unstable regions are printed with a thin line.
... Measured frequency response of the mechanically controlled oscillator.
... Schematic drawing of a rotary oscillator mechanically controlled by stoppers.
... Measured temperature dependence of the oscillator's phase with constant driving frequency and amplitude at the beginning of the plateau.