Networks of planar Hamiltonian systems

DOI10.1016/J.CNSNS.2017.05.008zbMATH Open1510.34107arXiv1701.03149MaRDI QIDQ6281824

David S. Tourigny

Publication date: 11 January 2017

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.

Mathematics Subject Classification ID

Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems (37J99) Synchronization of solutions to ordinary differential equations (34D06)

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