Spatio-temporal Unstable Chaotic Solutions of the Carleman Kinetic System

Abstract

The chaotic processes in time and space are investigated explicitly by means of solving the initial-boundary problem for the discrete kinetic equation. The Carleman model is studied. The physical interpretation of this kinetic system is presented. Numerical solutions show series of bifurcations when decreasing the Knudsen number. That leads to the period-doublings and then to the chaotic regimes with the positive senior Lyapunov exponential. The spatial oscillating profiles with the average solutions which differ from the steady profiles are observed. The chaotic character of the oscillations with intermittence is studied. This introduces a basic model for kinetic description of complicated physical processes.