Chaotic and quasiperiodic motions of three planar charged particles

We study two dynamical systems for the motion of three planar charged parti cles with charges n(j) epsilon {+/-1}, j = 1, 2, 3. Both dynamical systems are parametric with a parameter alpha is an element of [0, 1] and have the same nonlinear terms. As a = 0, 1, the dynamical systems have no chaos. How ever, one dynamical system may create chaos as a varies from zero to one. T his may provide an example to show that the homotopy deformation of dynamic al systems cannot preserve the long-time dynamics even though the dynamical systems have the same nonlinear terms.