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Background and Objectives: The van der Pole oscillator with an additional oscillatory circuit represents one of the simplest self-sustained oscillator system with two degrees of freedom. It is characterized by the phenomenon of frequency pulling, caused by the appearance of bistability and hysteresis. The bifurcation mechanism of pulling and bistability was previously identified, and the bifurcation analysis was carried out for the case of weak excitation when the system exhibits quasi-harmonic self-sustained oscillations. However, the question remains open about the influence of anharmonicity, which develops in the system with increasing excitation parameter, on the phenomenon of multistability and on the bifurcation mechanism of its formation. Is the effect of frequency pulling and the corresponding bistable states preserved over a wide range of values of the control parameters? Are new multistable states being formed? What does the bifurcation structure of the control parameter plane look like? In this paper, the above issues are studied using as an example a self-sustained oscillatory system consisting of the Rayleigh oscillator with an additional linear oscillator. Materials and Methods: Numerical simulation and bifurcation analysis of equilibrium states and limit cycles were performed using the XPPAUTO software package. Results: The results of a two-parameter analysis in a wide range of excitation and frequency detuning parameters have been presented, typical modes of self-sustained oscillations and their bifurcations have been described. Conclusion: It has been shown that the classical phenomenon of frequency pulling is observed only at small values of the excitation parameter of the system. The bistability region, where two limit cycles coexist, corresponding to in-phase and anti-phase oscillation modes in coupled oscillators, is bounded by both the detuning parameter and the excitation parameter.

On November 30, 2020, at the age of 78, Vadim S. Anishchenko suddenly died. He was Head of the Department of Radiophysics and Nonlinear Dynamics, Saratov State University (SSU), Doctor of Physics and Mathematics, Professor, Honored Scientist of the Russian Federation, Laureate of the International Science Prize of the Alexander von Humboldt Foundation, Honorary Worker of Education of the Russian Federation, Honorary Professor of SSU, world-class specialist in the field of nonlinear dynamics, founder of one of the leading scientific schools in radiophysics and nonlinear dynamics. The memories of people who knew Vadim S. Anishchenko closely at different periods of his life are published, as a tribute to the memory of an outstanding personality.

Background and Objectives: Studying the dynamical mechanisms of the emergence of nonlinear phenomena that are characteristic for multimode self-oscillating systems consisting of interacting oscillators and an ensemble of passive oscillators or representing active nonlinear systems with complex feedback channels is an important urgent task. The simplest example of a self-oscillating system with a complex feedback is the well-known classical van der Pol oscillator with an additional linear oscillatory circuit included in the feedback channel. We investigate the behavior of the multimode system increasing the number of oscillatory circuits in the oscillator’s feedback loop. The research in this paper can help to better understand the mechanisms of multistability formation in infinite-dimensional self-oscillating systems such as a generator with delayed feedback and a generator with distributed feedback. Materials and Methods: The system equations were derived for the electronic scheme of the self-oscillating system. To describe the existing dynamic modes by numerical simulation methods, the projections of the phase portraits and the Poincare sections were obtained. To study the mechanisms of formation of multistable states, the bifurcation analysis methods were used. Results: It was found that the mechanism underlying the multistability formation is based on a sequence of two supercritical Andronov – Hopf bifurcations and a subcritical Neymark – Saker bifurcation. Therefore, the multistability emerges as a result of gaining stability by the unstable limit set that existed before the multistability appears. Conclusion: The discovered mechanism of multistability formation opens up wide possibilities for managing the multistability, which are inaccessible for systems in which the multistability is realized through tangential bifurcations. In contrast to the tangential bifurcation, the subcritical Neymark – Sacker bifurcation assumes the existence of a limit cycle both before and after the bifurcation. Thus, it is possible to use a wide range of methods and tools to stabilize saddle limit cycles in order to control the boundaries of the multistability region in the space of control parameters of the system.

An analysis of publications has shown that mechanically clamped indexable inserts are predominantly used in modern tool manufacturing. Each insert has its shape and geometry in the tool coordinate system. The static system’s required geometry is achieved by the tilting of the insert pocket in the radial and axial directions. Therefore, it is of great importance in the tool design to know the relationships between the insert’s geometry parameters in the tool coordinate system where the geometry paraments of the insert are defined and working geometry parameters of the tool defined in the static coordinate system. The paper presents the developed methodology for determining the insert pocket base surface position to ensure the required values of the tool geometry parameters of the selected indexable insert in the static coordinate system. The graphs of the dependence of each of the angles of the insert geometry on the angles of rotation of this insert in the front and profile planes are presented as the level lines for practical use. Using these graphs, one can optimize all geometric insertion parameters in the static coordinate system. The model of the calculations of the mechanism of the insert clamping by a screw is developed. The basic size and tolerance of the output link determine the distance from the intersection line of the base surfaces to the thread axis on the pocket and the minimum amount of the screw stroke on the insert clamping in the pocket.

Reconstructive plastic (n = 24) and repair operations (n = 23) on the colon were performed in 47 patients at Coloproctology Research Center (Moscow). The patients were divided into 2 groups administered different anesthesias and postoperative analgesias: total intravenous anesthesia (TIA) and combined epidural anesthesia (CEA). Adequate analgesia by CEA and early activation of patients after the operation promoted earlier (by 2 days) recovery of the motor function of the intestine than after TIA and traditional intramuscular analgesia with a narcotic analgetic. CEA ensured complete blocking of nociceptive pulsation and neurovegetative protection a with lower doses of narcotics during the postoperative period and can be used in this type of operations and postoperative management. CEA prevented gastrointestinal pareses, improved microcirculation and metabolic processes at the zone of intervention, and decreased the incidence of postoperative complications.

The paper provides the results of a prospective epidemiological study of the prevalence of arterial hypertension in three populations: Chukotka's aborigines and migrants and a Novosibirsk's population. The most unfavourable epidemiological situation for arterial hypertension was found to be in migrant males aged 30-59 years. A medical examination is proposed among young migrants in the first years of adaptation in the North.

In the random sample of 762 males aged 30-59 years who had moved to Chukotka, the attitude towards their health, a physician, bad habits, and prevention of diseases was examined within the Programme on Epidemiology of Major Non-Communicable Diseases and Their Risk Factors among the residents of the Chukotsky Autonomous District. The non-aboriginal Chukotka's population having higher risk factors showed decreased self-appraisal of their health, inadequate awareness of their health and risk factors for diseases. However, the majority of the male population consider it useful to be surveyed, which should be borne in mind in implementing educational measures among these population groups.