Branching equation of Andronov-Hopf bifurcation under group symmetry conditions.
In branching theory of solutions of nonlinear equations group analysis methods [Ovsyannikov, Group Analysis of Differential Equations (Nauka, Moscow, 1978); Lectures on the Theory of Group Properties of Differential Equations (Novosibirsk University, Novosibirsk, 1966)] give the general approach for the construction of the complete form of branching equation and its subsequent investigation. These methods are applied here to the general situation of Andronov-Hopf bifurcation when there are some multiple semisimple eigenvalues on imaginary axis. (c) 1997 American Institute of Physics.
Loginov
B. V.
BV
Ulyanovsk State Technical University, 32 Severny Venets str., Ulyanovsk 432027, Russia.
Trenogin
V. A.
VA