The tools of weakly coupled phase oscillator theory have had a profound impact on the
neuroscience community, providing insight into a variety of network behaviours ranging from …

Robust heteroclinic networks are invariant sets that can appear as attractors in symmetrically
coupled or otherwise constrained dynamical systems. These networks may have a …

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 …

The Lotka–Volterra (LV) equations can be used to model the behaviour of complex systems
in nature. Trajectories in a stable heteroclinic channel (SHC) describe transient dynamics …

Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in
the form of attracting yet unstable saddle periodic orbits where units are synchronized into …

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 explore the effect of correlations between the in and out degrees of random directed
networks on the synchronization of identical pulse-coupled oscillators. Numerical …

The phenomenon of resonance will be dealt with from the viewpoint of dynamical systems
depending on parameters and their bifurcations. Resonance phenomena are associated to …

Symmetric networks of coupled dynamical units exhibit invariant subspaces with two or more
units synchronized. In time-continuously coupled systems, these invariant sets constitute …

We show that unstable attractors do not exist for smooth invertible dynamics. In systems
lacking these properties, we draw simple conclusions about their stability indices and look at …