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In present paper nonlinear oscillator driving by external force in a form of three harmonic signals with irrational ratios of the frequencies and the map of various dynamical regimes on the parameter plane are presented. The feature of tri-frequencies torus doubling and destruction are investigated.

In this letter we study nonlinear dynamics and transition to chaos in semiconductor superlattice coupled to external linear resonator. We have shown that such system demonstrates chaotic dynamics in wide range of supply voltage, whereas in autonomous superlattice only periodical dynamics exists. Revealed that transition to chaos in system goes through intermittency.

Experimental studies of stationary distributions of the electric ?eld intensity and the concentration of charge carriers in the Gunn diode have been provided by using near-?eld microwave microscope. The numerical computer calculation of these quantities based on the dependence of electrons mobility and di?usion coe?cient on the electric ?eld has been carried out. The existence of a multidomain mode of Gunn diodes has been found experimentally and con?rmed theoretically.

It is description of the way in which chemical environment of Briggs–Rauscher autooscillating reaction a?ects characteristics of oscillations. It has been ascertained that variations of the iodide complexes concentrations perhaps occurs due to increases of oxygen concentration in media and intermediate’s concentration ?uctuation. In?uence was investigated one of the basic natural oxidizing agent oxygen and it radical forms on autocooperative mechanisms of Briggs–Rauscher reaction.

In the work we consider the classic cyclic schemes for the construction of cognitive processes. Based on neurobiological data we indicate the need to introduce a special mechanism for adaptive control signals of a mismatch in cognitive processes at the stage preceeding the decision point. Endogenous opioid system can be considered one of the major neurochemical candidates for such «breakers». This system provides the suppression of signals about a mismatch between current and target states of the cognitive system.

We propose new mathematical models of the evolution of the human society based on the synergistic approach. They describe the dynamics of the indicators of the major integral development of the World-System such as the total population and the level of the technological development. Our models capture the basic laws of the space and temporal development of the society. They indicate the hyperbolic growth of the population that agrees with the demographical data and the cyclic dynamics.

This paper proposes a method of constructing of the ring system, in which the phenomena of complex analytical dynamics such as the Mandelbrot and Julia sets, are implemented in some approximation. The system is non-autonomous, includes frequency ?lters and nonlinear elements, described by the model of the resonant interaction of waves in quadratic nonlinear dispersive medium.

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.

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.

We study synchronization in ensembles of locally di?usive coupled Bonhoe?er–van der Pol oscillators. Individual elements frequencies in?uence on excitation propagation in one- and two-dimensional media is investigated. We show that excitation propagation speed depends on frequency mismatch between synchronization frequency and elements’ individual frequencies. Qualitative and quantitative results describing this e?ect are numerical modeling data and analytical research.