Dynamics of complex systems and its information aspects

A cycle of theoretical and experimental researches on spatio-temporal dynamics of ensembles consisting of active neurodynamic elements was carried out. Similarly to real neuronal ensembles, such systems are networks of interacting elements - "neurons" - localized in space. In contrast to the known "formal" neural networks, an element of a neurodynamical system possesses intrinsic, sometimes nontrivial dynamics. The phenomena of pattern formation, nonlinear wave propagation, phase cluster formation, fractal spatio-temporal structures of dynamic activity (fig. 1), and others were studied.

A universal control system based on neurodynamic principles of operation was proposed (fig. 2).


Fig. 1. Fractal structure of dynamic
activity

Fig. 2. Universal control system

Dynamical chaos in phase systems – generation, synchronization, transmission of information

Collective dynamics of small ensembles of coupled phase-controlled generators – phase-locked loop (PLL) systems – was investigated, including generation of chaotically modulated oscillations and controlling these oscillations so as to synchronize them and specify their features. It was demonstrated that integration of several PLL systems into an ensemble ensures bright opportunities for generation of chaotically modulated oscillations and controlling their properties. The results obtained on generation, synchronization of chaotically modulated oscillations in ensembles of coupled PLL systems, as well as on computer modeling of processes of information transmission by means of chaotic oscillations verify that these ensembles are suitable for constructing novel communication systems using dynamical chaos that ensure confidential transmission of information.

Fig. 3. Examples of attractor projections of a model PLL generator corresponding to the following modes: chaotically modulated oscillations (à), chaotic beats (b), oscillations with regular modulation (c), regular beats (d).
Fig. 4. Chaotically modulated oscillations in the first of two cascade-coupled PLL systems (physical experiment).
Fig. 5. Map of dynamic modes of two cascade-coupled PLL systems on the plane of parameters of the first generator (numerical experiment).