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This work is devoted to the Keldysh model of flutter suppression and rigorous approaches to its analysis. To solve the stabilization problem in the Keldysh model we use an analog of direct Lyapunov method for differential inclusions. The results obtained here are compared with the results of Keldysh obtained by the method of harmonic balance (describing function method), which is an approximate method for analyzing the existence of periodic solutions. The limitations of the use of describing function method for the study of systems with dry friction and stationary segment are demonstrated.
In the studies of dynamics of pathogens and their interactions with a host immune system, an important role is played by the structure of antigenic variants associated with a pathogen. Using the example of a model of antigenic variation in malaria, w
We investigate the behavior of the Generalized Alignment Index of order $k$ (GALI$_k$) for regular orbits of multidimensional Hamiltonian systems. The GALI$_k$ is an efficient chaos indicator, which asymptotically attains positive values for regular
We investigate the chaotic behaviour of multiparticle systems, in particular DNA and graphene models, by applying methods of nonlinear dynamics. Using symplectic integration techniques, we present an extensive analysis of chaos in the Peyrard-Bishop-
A `flutter machine is introduced for the investigation of a singular interface between the classical and reversible Hopf bifurcations that is theoretically predicted to be generic in nonconservative reversible systems with vanishing dissipation. In p
In this Letter we discussed the parametric instability of texture of homogeneous (in time) spin precession, explaining how spatial inhomogeneity of the texture may change the threshold of the instability in comparison with idealized spatial homogeneo