The bifurcational behaviour of the spatially distributed Rayleigh equation
Kazarnikov, Alexey (2013)
Diplomityö
2013
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe201306033791
https://urn.fi/URN:NBN:fi-fe201306033791
Tiivistelmä
At the present work the bifurcational behaviour of the solutions of Rayleigh
equation and corresponding spatially distributed system is being analysed.
The conditions of oscillatory and monotonic loss of stability are obtained. In
the case of oscillatory loss of stability, the analysis of linear spectral problem
is being performed. For nonlinear problem, recurrent formulas for the general
term of the asymptotic approximation of the self-oscillations are found, the
stability of the periodic mode is analysed. Lyapunov-Schmidt method is being
used for asymptotic approximation. The correlation between periodic solutions
of ODE and PDE is being investigated. The influence of the diffusion on the
frequency of self-oscillations is being analysed. Several numerical experiments
are being performed in order to support theoretical findings.
equation and corresponding spatially distributed system is being analysed.
The conditions of oscillatory and monotonic loss of stability are obtained. In
the case of oscillatory loss of stability, the analysis of linear spectral problem
is being performed. For nonlinear problem, recurrent formulas for the general
term of the asymptotic approximation of the self-oscillations are found, the
stability of the periodic mode is analysed. Lyapunov-Schmidt method is being
used for asymptotic approximation. The correlation between periodic solutions
of ODE and PDE is being investigated. The influence of the diffusion on the
frequency of self-oscillations is being analysed. Several numerical experiments
are being performed in order to support theoretical findings.