Internal energy exchanges and chaotic dynamics in an intrinsically coupled system

Intrinsically coupled nonlinear systems typically present different oscillating components that exchange energy among themselves. A paradigmatic example is the spring pendulum, for which we identify spring, pendulum, and coupled oscillations. We propose a new approach that properly accounts for the nonlinear coupling, and allows the analysis of energy exchanges among the different types of oscillation. We obtain that the rate of energy exchanges is enhanced for chaotic orbits. Moreover, the highest rates for the coupling occur in the vicinity of the homoclinic tangle of the primary hyperbolic point embedded in a chaotic sea. The results demonstrate a clear relation between internal energy exchanges and the dynamics of coupled systems, being an efficient new way to distinguish regular from chaotic orbits.