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Sergei P. Kurdyumov (1928–2004) and his distinguished contribution in the development of the modern interdisciplinary theory and methodology of study of complex self-organizing systems, i.e. synergetics, is under consideration in the article. The matter of a mathematical model of evolutionary dynamics of complex systems elaborated by him is demonstrated. The nonlinear equation of heat conductivity serves as a basis of the model.

Switching activity in the ensemble of inhibitory coupled Poicare systems is considered. The existence of heteroclinic contour in the phase space at the certain domain of parameter space has shown. Dynamics of the ensemble of non-identical inhibitory and di?usively coupled systems of Poincare is considered. The approximate bifurcation diagrams for all qualitatively di?erent regimes of the network activity have shown.

A numerical simulation of a wide band or secure communication scheme, based on nonlinear admixture of an information signal to the chaotic one, and on synchronization of the transmitter and receiver generators, manifesting hyperbolic chaos. Synchronization of the transmitter and receiver is provided by a strong unidirectional coupling between them. The study of the possibility of synchronization between subsystems and functionality of the communication scheme are presented.

One-parameter study of system of two nonlinearly coupled nonidentical Lang–Kobayshi oscillators is presented. The time delay in?uence on oscillation regimes in the system is studied. The posibility of periodic and quasiperiodic oscillations is shown. Variation of delay time leads to bifurcations and an alternation of periodic and quasiperiodic oscillations. Quasiperiodic oscillations are excited as a result of Neimark–Sacker bifurcation.

This work presents results of experimental studies of coherence resonance phenomenon in UHF devices with long interaction (TWT and BWO). Basic properties of this phenomenon were investigated. Discovered suppression e?ect of resonant response on external noise by external harmonic signal. This suppression e?ect can be used to increase signal-to-noise ratio in system’s output. Speci?c features of coherence resonance phenomenon in long-interaction devices also noted.

The e?ects of synchronization in the system of two coupled oscillators with delay are investigated. The picture of possible modes of generation in the case of identical and non-identical excitation parameters is studied in detail. The possibility of full synchro-nization in the stationary single-frequency, self-modulation and chaotic generation regime is demonstrated. The regime of «broadband synchronization» is found. In contrast with coupled ?nite dimensional systems, the boundaries of broadband synchronization area have wavy form.

E?ect of re?ection from the remote load on the mode competition in a two-mode electronic maser is considered. A system of quasilinear equations for slowly varying amplitudes of the modes with cubic nonlinearity where the e?ect of re?ections is taken into account by time delayed terms is analyzed. The most typical case of competition of two modes with close frequencies at the centre of generation zone is studied in detail.

The e?ect of a weak nonlinear dissipation on the structure of the system’s phase space with stochastic web is invstigated. The bifurcation scenario of attractor transformations with the increase of dissipation is revealed.

Experimental investigation results of the nonautonomous active ring system based on a ferromagnetic ?lm at three-wave interactions were considered. The possibility of system dynamics controlling by the external harmonic signal was shown. A comparison of experimental data with simulation results was done.

The problem of compact mathematical model reconstruction of short electroencephalogram tracings during epileptic seizure is solved. This kind of model map can be useful in many applications, for example, in time series segmentation with following clustering of obtained fragments. Optimization methods are proposed as a solution. It is shown that application of optimization methods allows to obtain adequate model at that time decreasing number of modeling map basis functions.