Hamiltonian and dissipative dynamics are two main realms of chaos theory. In this talk, I report on a setup where these two cases interplay . I start with a classical Hamiltonian system of a particle moving in an external potential. Adding activity to the particle motion makes the dynamics dissipative, with a possibility for a strange attractor in the dynamics. However, in the overactive limit, where the activity is very strong, the system is again Hamiltonian (although with a quite non-trivial Hamilton function). Such an overactive particle can demonstrate chaotic or quasiperiodic dynamics. For an interaction of several particles, one often assumes aligning forces that are dissipative. Now, the collective dynamics becomes dissipative and leads to synchronization of particles. In the synchronous regime, the alignment does not work, and the final dynamics is again Hamiltonian.
 I. Aranson & A. Pikovsky, Confinement and collective escape of active particles, Physical Review Letters, 128, 108001, 2022.