The analysis of bifurcations in the spatially distributed Langford system
Klimov, Sergey (2013)
Diplomityö
2013
Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi-fe201306033792
https://urn.fi/URN:NBN:fi-fe201306033792
Tiivistelmä
In this thesis the bifurcational behavior of the solutions of Langford system
is analysed. The equilibriums of the Langford system are found, and the
stability of equilibriums is discussed. The conditions of loss of stability are
found. The periodic solution of the system is approximated. We consider
three types of boundary condition for Langford spatially distributed system:
Neumann conditions, Dirichlet conditions and Neumann conditions with additional
requirement of zero average. We apply the Lyapunov-Schmidt method
to Langford spatially distributed system for asymptotic approximation of the
periodic mode. We analyse the influence of the diffusion on the behavior of
self-oscillations. As well in the present work we perform numerical experiments
and compare it with the analytical results.
is analysed. The equilibriums of the Langford system are found, and the
stability of equilibriums is discussed. The conditions of loss of stability are
found. The periodic solution of the system is approximated. We consider
three types of boundary condition for Langford spatially distributed system:
Neumann conditions, Dirichlet conditions and Neumann conditions with additional
requirement of zero average. We apply the Lyapunov-Schmidt method
to Langford spatially distributed system for asymptotic approximation of the
periodic mode. We analyse the influence of the diffusion on the behavior of
self-oscillations. As well in the present work we perform numerical experiments
and compare it with the analytical results.