Applied Problems of Nonlinear Oscillation and Wave Theory

Subject of the study. The bifurcations of the attracting sets of the deformational displacement of the tool in the dynamic system of the turning machine depending on the beats periodic trajectory of the spindle group are considered in the article. The dynamic system is represented by the two interact mechanical subsystems through the dynamic link formed by the cutting process.

Processes of the El Ni  ̃no – Southern Oscillation (ENSO) are investigated based on the mathematical theory of the so-called the strange nonchaotic attractor (SNA) in the quasiperiodically forced dynamic systems, and using the sea surface temperature and the atmospheric sea-level pressure data for the 1870–2014 year period.

The problem of ultrawideband chaotic radio pulse propagation through the media within

living organisms is considered in this article. This area gains relevance due to the increase of

Ideas of temporary energy distributions of large-scale atmospheric motions are made more accurately in the range of scales from days to one year in order to solve the problem of the chaos and order co-existence in the weather and climate dynamics. Spectra of the Blinova’s mean and shifted zonal extratropical flow indices as well as spectra of the tropical Southern Oscillation and El Ni  ̃no indices are used for this purpose.

In the proposed paper, we investigate the dynamical behavior of the modified system with frequency-phase control, which uses two-channel discriminator in the circuit of phase control and multi-frequency discriminator with periodic nonlinearity in the circuit of frequency control. We consider the case of identical low-pass filters of the third order in the both control circuits.

На основе асимптотических методов Боголюбова для динамической модели Гарела-Росслера показана возможность автоколебательных режимов в существовании последовательности бифрукаций удвоения периода. Качественные результаты подтверждаются численными исследованиями.

In this article we consider simulation of appearance oscillations in abundance of biological species and concomitant abrupt changes in the population development process. The inductors for the appearance of many long-period fluctuations, such as herring cycles in the Pacific Ocean, have not yet been fully established. Changes in population cycles can take extreme nature and violate prevailing uniformity of biological diversity, even evoke significant impacts on ecosystems.