By G. A. Leonov, I. M. Burkin, A. I. Shepeljavyi (auth.)
This e-book is dedicated to nonlocal concept of nonlinear oscillations. The frequency equipment of investigating difficulties of cycle lifestyles in multidimensional analogues of Van der Pol equation, in dynamical structures with cylindrical part house and dynamical structures pleasing Routh-Hurwitz generalized stipulations are systematically offered the following for the 1st time.
to unravel those difficulties equipment of Poincaré map development, frequency tools, synthesis of Lyapunov direct equipment and bifurcation idea components are utilized. V.M. Popov's approach is hired for acquiring frequency standards, which estimate interval of oscillations. additionally, an method of examine the steadiness of cycles in accordance with the information of Zhukovsky, Borg, Hartmann, and Olech is gifted, and the results showing whilst bounded trajectories are risky are mentioned. For chaotic oscillations theorems on localizations of attractors are given. the higher estimates of Hausdorff degree and size of attractors generalizing Doudy-Oesterle and Smith theorems are bought, illustrated via the instance of a Lorenz approach and its varied generalizations.
The analytical equipment constructed within the ebook is utilized to the research of oscillation of assorted keep an eye on structures, pendulum-like platforms and people of synchronization.
Audience: This quantity could be of curiosity to these whose paintings contains Fourier research, international research, and research on manifolds, in addition to arithmetic of physics and mechanics often. A heritage in linear algebra and differential equations is thought.