ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

Прикладные задачи нелинейной теории колебаний и волн

Influence of the choice of the model structure for working capacity of nonlinear granger causality approach

Currently, the method of nonlinear Granger causality is actively used in many applications in medicine, biology, physics, to identify the coupling between objects from the records of their oscillations (time series) using forecasting models. In this paper the impact of choosing the model structure on the method performance is investigated. The possibility of obtaining reliable estimates of coupling is numerically demonstrated, even if the structure of the constructed forecasting model differs from that of the reference system.

On the period-multiplying bifurcation of glacial cycles in the pliocene – pleistocene

In the Pliocene (about ?ve – two million years before present) global climate ?uctuated with a period corresponding well 41-thousand-year cycle of changes in the Earth’s axis inclination to the ecliptic plane. Then, this period has disappeared, despite the fact that the 41-thousand-year cycle even slightly increased its scope and, therefore, the response to it would have only strengthened. By analyzing paleoclimatic series covering the Pliocene and subsequent Pleistocene, we show that the response of the climate system simply became unstable and therefore unobservable.

Nonlinear dynamics and acoustic signals generated by periodic impacts of corundum probe on the solid surface

Experimental and theoretical study of nonlinear dynamics and acoustic signals generated by periodic impacts of corundum probe on the solid surface are conducted. In the work two models are considered for the description of experiments: the analytical model based on the laws of conservation of energy and momentum; the model based on the numerical solution of the nonlinear equation of probe motion. It is shown that the acoustic signal amplitude increases in direct proportion to the oscillations probe amplitude.

Subharmonic resonance in a system of two dissipative coupled van der pol oscillators with external force

The problem of the excitation of two coupled oscillators is discussed in the case of the simple subharmonic resonance between the external force and eigen-frequencies of the oscillators. The corresponded phase equation is obtained.

The study of the unidirectionally coupled generators of robust chaos and wide band communication scheme based on its synchronization

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.

Mutual synchronization of two coupled generators with delay

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.

Effect of delayed reflection from the remote load on mode competition in а gyrotron

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.

Studies of scale invariant change-over dynamics in the hierarchical model of defects development

Hierarchical model of defect development makes possible the consideration of both ordinary and self-organized criticality from the common viewpoint. Scale invariant critical state in this model is presented by ?xed points of a renormalization transformation, connected with lifting to the next level of hierarchy. So stable ?xed points of the transformation correspond to the self-organized criticality and unstable points correspond to the ordinary one.

Chaotic microwave pulse train generation in self-oscillatory system based on a ferromagnetic film

Experimental investigations results of the ring self-oscillatory system based on a ferromagnetic ?lm at three-wave interactions were considered. The model describing this system was constructed. The typical regimes of a generation, including generation of the chaotic microwave train were calculated with the help of the constructed model. The numerical simulations and experimental results had a good agreement.

Nonlinear effects in autooscillatory system with frequency- phase control

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.