BIFURCATIONS IN BIPARAMETRIC QUADRATIC POTENTIALS .2.

Quadratic Hamiltonians with the phase space on the L(2) sphere represe nt numerous dynamical systems. There are only two classes of quadratic Hamiltonians depending on two parameters. We analyze the occurrence o f bifurcations and we obtain the bifurcation lines in the parameter pl ane for one of these classes, thus complementing the work done in a pr evious paper where the other class was analyzed. As the parameters evo lve, the appearance-disappearance of homoclinic orbits in the phase po rtrait is governed by four types of bifurcations: namely the pitchfork , the butterfly, the oyster and the pentadent bifurcations. We find al so values where the system is degenerate, that is, there are nonisolat ed equilibria. (C) 1995 American Institute of Physics.