Konstantin Koshel'

The appearance of chaotic regimes near elliptic point in a cell of particles’ chain interacting by means of Lennard–Jones potential is studied. The threshold nature of chaotization advent in the case of single-frequency cell excitation is demonstrated. A method of global chaotization based on multifrequency external excitation is proposed. The results of numerical experiments show that in this case the formation of global chaos is achieved at essentially lower values of external excitation amplitude and frequency, than in the case of single frequency excitation.

We consider a model of a point vortex in a two-layer quasi-geostrophic flow. In this model, the chaotization of the phase space strongly depends on the frequency of the external excitation. Numerical experiments show that the degree of chaotization as a function of the excitation frequency has a number of pronounced extrema. Upon examination of rotation frequencies of fluid particles and the corresponding non-linear resonances, we have found a strong connection between these extrema and disappearance of the non-linear resonances. This disappearance phenomenon has been studied using the Poincare surface-of-section technique.