Coupled Networks, Patterns and Complexity - Abstract

Timme, Marc

Heteroclinic switching and universal computation via complex networks of saddles

Over the last decade, the field of complex network dynamics has attracted considerable interest through analyzing the dynamics of networks of coupled dynamical units. Here we study complex network dynamics on a higher level of abstraction: the dynamics close to heteroclinic networks of saddle states of a system. Complex networks of dynamically connected saddle states persistently emerge in a broad range of high-dimensional systems and may reliably encode inputs as specific switching trajectories. Their computational capabilities, however, are far from being understood. Here, we analyze how symmetry-breaking inhomogeneities naturally induce predictable persistent switching dynamics across such networks. We show that such systems are capable of computing arbitrary logic operations by entering into switching sequences in a controlled way. This dynamics thus offers a highly flexible new kind of computation based on switching along complex networks of states.
References:
Ashwin and Timme, Nonlinearity 18:2035 (2005); Nature 436:36 (2005);
Schittler Neves and Timme, J. Phys. A: Math. Theor. 42:345103 (2009); Phys. Rev. Lett. 109, 018701 (2012)