The purpose of this work is to research the phenomena of the self-oscillation and the synchronization for the model of business and financial oscillator, which presented as the system of automatic control. Methods. The research methods are the qualitative and numerical methods of the theory of nonlinear dynamical systems and the theory of the bifurcations. Results. This work presents the model of business and financial oscillators as the phase-controlled oscillator and as the frequency-controlled oscillator.
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.
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.
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.
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.
Wireless sensor networks that is a fast emerging branch of modern telecommunications are considered in this paper. Particular attention is paid on ultrawideband sensor networks where chaotic radiopulses are used as an information carrier between sensor nodes. Development of such wireless sensor networks became possible after longterm investigations of chaotic oscillations and chaos 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.
