We study a finite-dimensional "collective coordinates" model. We use dynamical systems and matched asymptotic expansions to explain the two-bounce resonance phenomenon originally investigated in collisions between kink and antikink traveling waves by Campbell. We derive the critical relative velocity below which the interacting kinks have complex behavior, which agrees with our accurate numerical simulations. We derive a separatrix map that explains the complex fractal-like dependence on initial velocity for kink-antikink interaction. Joint work with Roy H. Goodman.