Title: Networks of planar Hamiltonian systems,
Abstract: 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.