The cycling effect of coupled particle and energy feedback in nuclear reaction systems is considered. Nonlinear dynamical equations for the evolution of interacting particle populations and their associated mean kinetic energies are formulated for a finite reaction domain. Selected low-order reductions and specifications applicable to some nuclear fuel cycles are examined for their dynamic trajectories in phase-space. In order to identify typical chain characteristics we classify particle and energy chaining on the basis of a generalized kinetic formulation. Consideration of both these reaction sustaining mechanisms leads inevitably to nonlinear dynamics behaviour.