Functional oscillator networks, such as neuronal networks in the brain, exhibit switching
between metastable states involving many oscillators. We give exact results how such …

The well-known game of Rock–Paper–Scissors can be used as a simple model of
competition between three species. When modelled in continuous time using differential …

Coupled populations of identical phase oscillators with higher-order interactions can give
rise to heteroclinic cycles between invariant sets where populations show distinct …

We consider a heteroclinic network in the framework of winnerless competition, realized by
generalized Lotka-Volterra equations. By an appropriate choice of predation rates we …

Dynamical systems on graphs can show a wide range of behaviours beyond simple
synchronization-even simple globally coupled structures can exhibit attractors with …

Heteroclinic networks and cycles are invariant sets comprised of interacting nodes
connected by heteroclinic trajectories. Often the sets are not asymptotically stable but attract …

Heteroclinic computing offers a novel paradigm for universal computation by collective
system dynamics. In such a paradigm, input signals are encoded as complex periodic orbits …

We address the level of complexity that can be observed in the dynamics near a robust
heteroclinic network. We show that infinite switching, which is a path towards chaos, does …

Dynamical systems containing heteroclinic cycles and networks can be invoked as models
of intransitive competition between three or more species. When populations are assumed …

Homoclinic and heteroclinic connections can form cycles and networks in phase space,
which organize the global phenomena in dynamical systems. On the one hand, stability …