Autonomous oscillations

According to this model it should also be possible to initiate propagating reaction fronts even if the system does not oscillate autonomously, by a... 

The use of this theory in studies of nonlinear oscillations was suggested in 1929 (by Andronov). At a later date (1937) Krylov and Bogoliubov (K.B.) simplified somewhat the method of attack by a device resembling Lagrange s method of the variation of parameters, and in this form the method became useful for solving practical problems. Most of these early applications were to autonomous systems (mainly the self-excited oscillations), but later the method was extended to... 

Autonomous (A) Versus Nonautonomous (NA) Problems. Practically all nonlinear problems of the theory of oscillations reduce to the differential equation of the form... 

There are two major classes of problems to be investigated (NA) nonautonomous, and (A) autonomous.15 In each of these two classes appear two subclasses (NR) nonresonance oscillations, and (R) resonance oscillations. The treatment of these cases is slightly different. 

Arcsine distribution, 105, 111 Assumption of molecular chaos, 17 Asymptotic theory, 384 of relaxation oscillations, 388 Asynchronous excitation, 373 Asynchronous quenching, 373 Autocorrelation function, 146,174 Autocovariance function, 174 Autonomous problems, 340 nonresonance oscillations, 350 resonance oscillations, 350 Autonomous systems, 356 problems of, 323 Autoperiodic oscillation, 372 Averages, 100... 

Besides the two main characteristics of sensitivity as well as specificity of a sensor, the industrial, military, and other standards demand the device to be portable, economical, autonomous, and power efficient. In order to address some of these characteristics, the authors in their respective laboratories have been working on improving the design of the prototype, as shown in Figs. 15.6 and 15.7, respectively. The necessaiy electronics consisting of local oscillators, beat oscillators, smaller cavities, mixers, and phase-locking loops have been assembled in prototypes. As of this date the device needs further evaluation in an operational environment to establish a set of encyclopedic data and for comparison with unknown toxins. 

Assumptions 1 to 5 as in model 13. The state of the chemical neuron is allowed to change only at discrete times, dictated by an autonomously oscillating catalyst e. The concentration of e is very small except during short intervals, e interacts with Aj or of each neuron, and rapid equilibrium occurs when its... 

Numerical simulations indicate that relay of cAMP pulses represents a different mode of dynamic behavior, closely related to oscillations. Just before autonomous oscillations break out, cells in a stable steady state can amplify suprathreshold variations in extracellular cAMP in a pulsatory manner. Thus, relay and oscillations of cAMP are produced by a unique mechanism in adjacent domains in parameter space. The two types of dynamic behavior are analogous to the excitable or pacemaker behavior of nerve cells. 

The periodic recurrence of cell division suggests that globally the cell cycle functions like an autonomous oscillator. An extended model incorporating the sequential activation of the various cyclin-dependent kinases, followed by their inactivation, shows that even in the absence of control by cell mass, this sequence of biochemical events can operate as a limit cycle oscillator [145]. This supports the union of the two views of the cell cycle as dominoes and clock [146]. Because of the existence of checkpoints, however, the cell cycle stops at the end of certain phases before engaging in the next one. Thus the cell cycle looks more like an oscillator that slows down and makes occasional stops. A metaphor for such behavior is provided by the movement of the round plate on the table in a Chinese restaurant, which would rotate continuously under the movement imparted by the participants, were it not for frequent stops. 

Neurons of the mammalian suprachiasmatic nucleus (SCN) contain cell-autonomous, self-sustained oscillators, which are able to maintain circadian periodicity even when isolated in vitro or when the animal is placed under... 

The relationship between central and peripheral oscillators is different in flies and mammals. In mammals, these oscillators form a hierarchy in which the central oscillator, which resides in the suprachiasmatic nucleus (SCN), functions as a master clock that is entrained by photic signals from the eye, and in turn drives subservient peripheral oscillators via humoral signals (Moore et al 1995, Yamazaki et al 2000, Kramer et al 2001, Cheng et al 2002). In contrast, both central and peripheral oscillators operate autonomously and are directly entrainable by light in Drosophila (Plautz et al 1997), thus obviating the need for a hierarchical system. Our results support the concept of independent oscillators in flies since central (sUN ) oscillators are not necessary for olfaction rhythms and local oscillators in antennae appear to be sufficient. 

Although the molecular analyses draw the common molecular mechanism for the mammalian SCN oscillation, there are topographic differences among SCN cells. mPer1 and mPer2 in dorsomedial cells showed a strong autonomous expression with no light response, while those in ventrolateral cells showed a... 

Weit Joe Takahashi, is your expectation that you would only see this at the tissue level The idea is presumably that in a cell-autonomous sense, period and phase are still coupled because of the way we imagine the oscillator works, but when you are now talking about how a collection of coupled oscillators integrate this into behavioural outputs, there are now other factors that must come into play. Is this fair to say Is it only in the chimeras, and not in the heterozygotes, that you see these unusual combinations and dissociations of phase and period ... 

This system in its linear version (i.e., when e = 0) is a dynamical filter. Suppose that the oscillators interact with each other with the interaction parameter a = 0.9. The frequency 00 of the external driving field varies in the range 0 < < 4.2. The other parameters of the system are A 200, coq 1, c 0.1, and = 0.05. The autonomized spectrum of Lyapunov exponents A-4, >,5 versus the frequency to is presented in Fig. 23. In the range 0 < < 0.2 the system does not exhibit chaotic oscillation. Here, the maximal Lyapunov exponent Xi = 0 and the spectrum is of the type 0, —, —, —, (limit cycles). 

Potentiometric techniques have been used to study autonomous reaction rate oscillations over catalysts and carbon monoxide oxidation on platinum has received a considerable amount of attention43,48,58 Possible explanations for reaction rate oscillations over platinum for carbon monoxide oxidation include, (i) strong dependence of activation energy or heat of adsorption on coverage, (ii) surface temperature oscillations, (iii) shift between multiple steady states due to adsorption or desorption of inert species, (iv) periodic oxidation or reduction of the surface. The work of Sales, Turner and Maple has indicated that the most... 

We now have a total of six parameters four from the autonomous system (p, r0, and the desorption rate constants k, and k2) and two from the forcing (rf and co). The main point of interest here is the influence of the imposed forcing on the natural oscillations. Thus, we will take just one set of the autonomous parameters and then vary rf and co. Specifically, we take p = 0.019, r0 = 0.028, fq = 0.001, and k2 = 0.002. For these values the unforced model has a unique unstable stationary state surrounded by a stable limit cycle. The natural oscillation of the system has a period t0 = 911.98, corresponding to a natural frequency of co0 = 0.006 889 6. 

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