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

динамический хаос

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.

Destruction of the coherent mode in system of two oscillators at the strong resonant mutual couplings

The hypothesis about destruction of a coherent mode in system of two mutual couplings microwave oscillators is examine, each of which in a stand­alone mode generates stable unifrequent oscillations. It is experimentally shown, that at strong resonant couplings synchronous oscillations are unstable, therefore the system go over in in a mode of dynamic chaos.

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 chaos: the difficult path discovering

Dynamic chaos – a remarkable milestone development of science of the last centuryhas attracted the attention of different areas of knowledge. Chaos theory describes not only a wide range of phenomena in various fields of physics and other natural sciences and penetrates into the humanitarian sphere, but also significantly influenced the scientific picture of the world.

Bifurcations and oscillatory modes in complex system with phase control

The results are produced of research of dynamical modes and bifurcation in a complex system with phase control, based on mathematical model with two degrees of freedom in the cylindrical phase space. The location of domains corresponding to different dynamical states of the system is established. The processes developing in the system as a result of loss stability of the synchronous mode, and scenarios of evolution of nonsynchronous modes under variation of system parameters are investigated.

Origin of intermittency in singular hamiltonian systems

In the paper we studied properties of conservative singular maps. It was found that under some conditions the intermittency without chaotic phases can be observed in these maps. The alternative mechanism of the intermittency origin in Hamiltonian singular systems was considered. Its general properties were discussed. We studied special properties of phase space structure in these systems. It is shown that Hamiltonian intermittency can be characterized by zero Lyapunov exponents. It gives us the possibility to classify it as pseoudochaos dynamics.

A neural network as a predictor of the discrete map

The possibility of predicting the regular and chaotic dynamics of a discrete map by using artificial neural network is studied. The method of error back­propagation is used for calculation the coefficients of the multilayer network. The predicting properties of the neural network are explored in a wide region of the system parameter for both regular and chaotic behaviors. The dependance of the prediction accuracy from the degree of chaos and from the number of layers of the network is studied.

The averaging method, a pendulum with a vibrating suspension: N.N. Bogolyubov, A. Stephenson, P.L. Kapitza and others

  The main moments of the historical development of one of the basic methods of nonlinear systems investigating (the averaging method) are traced. This method is understood as a transition from the so-called exact equation: dx/dt = ?X(t, x),     ? ? is small parameter, to the averaging equation d?/dt= ?X0(?) + ?2P2(?) + ...?mPm(?) by corresponding variable substitution. Bogolyubov–Krylov’s approach to the problem of justifying the averaging method, based on the invariant measure theorem, is analyzed.