RESUMEN
The response of a weakly damped bistable oscillator to an external periodic force is considered theoretically. In the approximation of weak signals we can write a linearized equation for the signal and the corresponding nonlinear equation for the noise. These equations contain two unknown parameters: An effective stiffness and an additional damping factor. In the case of the weakly damped bistable oscillator, considered here, the two-dimensional Fokker-Planck equation corresponding to the equation for the noise can be solved approximately by changing to a slow variable ("energy") and applying a method of successive approximation. This approach allows us to find the unknown parameters and to calculate the amplitude ratio of the output and input signals, i.e., the gain factor.
RESUMEN
We consider an overdamped bistable oscillator subject to the action of a biharmonic force with very different frequencies, and study the response of the system when the parameters of the high-frequency force are varied. A resonantlike behavior is obtained when the amplitude or the frequency of this force is modified in an experiment performed by means of an analog circuit. This behavior, confirmed by numerical simulations, is explained on the basis of a theoretical approach.
RESUMEN
We study here the different modes of self-oscillations in ring Toda chains with Rayleigh-type negative friction. Assuming that at small friction the shape of self-oscillations is close to one of the known Toda solitonlike solutions we use analytical methods in combination with numerical ones for study of the self-oscillations. We calculate explicitly for a Toda chain consisting of N elements the N+1 different modes of self-oscillations. Among them two modes correspond to left and right rotations of the chain as a whole with a constant velocity Each of the other N-1 modes represents a combination of solitonlike oscillations and a rotation with a velocity depending on the mode number. Only for the mode corresponding to antiphase oscillations of the chain neighboring elements (such oscillations are possible for an even N) the constant component of the velocity is equal to zero.
RESUMEN
Two systems, which are models of biological processes, are considered. These systems are notable for responding to different external actions nearly alike. This is associated with the fact that an external action excites only their natural intrinsic motions. Two kinds of external actions, harmonic and random, are studied. It is shown that each of them induces a transition to a new state that can be treated as a peculiar kind of phase transitions. Characteristics of these phase transitions are found.
Asunto(s)
Brotes de Enfermedades , Modelos Biológicos , Niño , Enfermedades Transmisibles/epidemiología , Enfermedades Transmisibles/transmisión , Humanos , Modelos Estadísticos , Dinámicas no Lineales , Estaciones del AñoRESUMEN
A modification of the Mackey-Glass model for a respiration control system is proposed. The equations corresponding to the proposed model were built. A solution of the equations was obtained, which corresponds to the Cheyne-Stokes irregular respiration.