Networks of planar Hamiltonian systems
  We introduce diffusively coupled networks where the dynamical system at each
vertex is planar Hamiltonian. The problems we address are synchronisation and
an analogue of diffusion-driven Turing instability for time-dependent
homogeneous states. As a consequence of the underlying Hamiltonian structure
there exist unusual behaviours compared with networks of coupled limit cycle
oscillators or activator-inhibitor systems.
