ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


фазовые портреты

Nonlinear effects in autooscillatory system with frequency- phase control

Dynamical modes and nonlinear phenomena in the models of oscillatory system with frequency-phase control in the case of periodic nonlinear characteristics of frequency discriminator are investigated. Stability of synchronous mode is analyzed. The existences of a great number various periodic and chaotic nonsynchronous modes are established. Peculiarities of the system dynamics caused by parameters of frequency control loop are considered.

Regular and chaotic dynamics of two-ring phase locked system part 1 dynamics of frequency-phase system with identical first-order filters in control circuits

We present the results of investigation of dynamical modes in the model of oscillatory system with frequency-phase control using multi-frequency discriminator inversely switched in the chain of frequency control. The study was carried out on the basis of mathematical model of the system with one degree of freedom with the use of qualitative and numerical methods of nonlinear dynamics. It is shown that in such a system may be realized both synchronous and great number of non-synchronous periodic modes.

Regular and chaotic dynamics of two-ring phase locked system part 2 peculiarities of nonlinear dynamics of frequency-phase system with identical third-order filters in control circuits

The results of investigation of dynamical modes in the model of oscillatory system with  frequency-phase control using multi-frequency discriminator inversely switched inthe chain of  frequency control are presented. The study was carried out on the basis of mathematical model of  the system with two degrees of freedom with the use of qualitative and numerical methods of nonlinear dynamics. It is shown that in such a system may be realized both synchronous and great  number of non-synchronous periodic and chaotic modes of different complexity.

Dynamical modes and nonlinear phenomena in modified autooscillatory system with frequency-phase control

In the proposed paper, we investigate the dynamical behavior of the modified system with frequency-phase control, which uses two-channel discriminator in the circuit of phase control and multi-frequency discriminator with periodic nonlinearity in the circuit of frequency control. We consider the case of identical low-pass filters of the third order in the both control circuits. Mathematical model of analyzed frequency-phase system is presented by a nonlinear dynamical system in the four-dimensional cylindrical phase space.