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First order (three-magnon) parametric instability of magnetostatic surface waves (MSSW) was experimentally studied in two-dimensional (2D) magnonic crystals with rhombic and square lattices with lattice parameter 37–40 mm. The instability was produced by etching of holes 32 mm in diameter and 1–2 mm in depth in the 16 mm-thick yttrium iron garnet (YIG) film. It was found, that MSSW threshold powers for parametric instability development in case of 2D magnonic crystals are of the order of two times greater than analogous threshold values for starting YIG films.

It was shown experimentally that at synchronization of chaotic oscillation in the microwave active resonance oscillators the following effects take place: own chaotic dynamics suppression; periodic oscillation establishing; the frequency capture by external harmonic signal, and noticeable power decrease of these oscillation.

We present the results of investigation of dynamical regimes in the models of oscillatory systems with frequency and frequency-phase control. The processes of excitement of nonsynchronous regimes and transitions between them are considered. A special attention is given to the study of the origin and stages of development of deterministic chaos in these systems. The existence of several types of chaotic attractors is established. Various scenarios of transition from regular dynamical regimes to chaotic ones under variation of the systems parameters are analyzed.

Dynamics of two phase-locked-loop systems with low-inertia control loops coupled through the phase discriminator is investigated. Stability of synchronous modes of the ensemble is considered. Mechanisms of arising of quasi-synhronous oscillations are studied. Domains of existence of synchronous and quasi-synhronous modes are analysed.

The development of a gas pool and operation of an underground gas storage facility are studied as dynamic systems with use of concepts and terms of nonlinear dynamics. For the first time bifurcation diagrams have been constructed for nonlinear dynamic models of a gas pool and an underground gas storage facility. Stability conditions of the processes  of the gas pool development and of the underground gas storage facility functioning have been studied.

The gas pool and underground gas storage facility are simulated as nonlinear dynamic systems. For the first time the basic physic and mathematical models of gas density oscillations during the development of a gas pool and operation of an underground gas storage facility have been worked out. It is shown that the occurrence of oscillations is connected with heterogeneity of the reservoir, gas cross-flows between heterogeneity elements, and finiteness of velocity of gas pressure disturbances propagation in the reservoir bed.

In present paper the following effects in nonlinear oscillator with final dissipation are studied: stochastic resonance, stochastic synchronization and noise-induced chaos. It is shown that stochastic resonance and stochastic synchronization at final dissipation have the same regularities as in the case of overdamped oscillator but are observed at a lower noise level.

Problems in describing chaotic phase synchronization are connected with ambiguity of definition of istantaneous phase as well as with limiting of its applicability by the coherent chaos regime. We demonstrate that this phenomenon can be analysed by means of function of mutual coherence which has not these restrictions.

In the work the influence of time delay of coupling on the complete synchronization of chaos in an interacting systems with discrete time is studied. The system’s behavior is considered in dependence on coupling coefficient value and delay time value. It is established that coupling with time delay prevents appearance of the complete synchronization of chaos, however it allows the synchronization of periodic and quasi-periodic oscillations.

A two-dimensional model exhibiting the chaotic spiking-bursting activity of real neurons is proposed. The model is given by the discontinuous two-dimensional map. It is constructed on the basis of the discrete modification of the FitzHugh–Nagumo model and one-dimensional Lorenz type map. We have studied the dynamics of the system, found the conditions on the parameters under which chaotic attractor exists. The structure and properties of the attractor is studied. This attractor mimics spiking-bursting oscillations.