Controlling the Time Evolution of Paths in a Hierarchical Heteroclinic Network
A heteroclinic network is a sequence of trajectories connecting saddles in a topological network. Although this particular nonlinear dynamics looks exceptional, it is frequently found in ordinary differential equations under certain constraints like symmetries or delay. Accordingly it is predicted in models of coupled phase oscillators, pulse-coupled oscillators and models of winnerless competition. The applications range from social systems to ecological systems, fluid mechanics, chemostats, computation to neuronal networks.