In this thesis I considered the dynamics of self-propelling particles (SPP). Flocking of living organisms like birds, fishes, ants, bacteria etc. is an area where the theory of the collective... Show moreIn this thesis I considered the dynamics of self-propelling particles (SPP). Flocking of living organisms like birds, fishes, ants, bacteria etc. is an area where the theory of the collective behaviour of SPP can be applied. One can often see how these animals develop coherent motion, amazing the observer by the diversity of its forms and shapes. In this thesis a hydrodynamic model with so-called kinematic constraints, which are imposed on the orientations of the velocities of the particles, is proposed. The tendency of the particles to adjust their velocities to the ones of the neighbours leads to the emergence of a coherent motion. In our model two types of stationary flows are obtained: linear and vortical hydrodynamic flows. A remarkable property of the vortical flow is that it has finite flocking behaviour, where the density and the velocity fields are coupled. From the physical point of view these flows are of interest because of their realization in nature. The stability properties of the stationary flows are determined. Further a hydrodynamic model is derived from the discrete description using the averaging procedure. The connection between the discrete and continuous approaches is analysed. Show less
