Systems of dynamical elements exhibiting spontaneous rhythms are found in various fields
of science and engineering, including physics, chemistry, biology, physiology, and …

Investigating the dynamics of a network of oscillatory systems is a timely and urgent topic.
Phase synchronization has proven paradigmatic to study emergent collective behavior …

The dynamical systems found in nature are rarely isolated. Instead they interact and
influence each other. The coupling functions that connect them contain detailed information …

Modern air vehicles perform a wide range of operations, including transportation, defense,
surveillance, and rescue. These aircraft can fly in calm conditions but avoid operations in …

The applicability of phase models is generally limited by the constraint that the dynamics of a
perturbed oscillator must stay near its underlying periodic orbit. Consequently, external …

While phase reduction is a well-established technique for the analysis of perturbed limit
cycle oscillators, practical application requires perturbations to be sufficiently weak thereby …

Many challenging problems that consider the analysis and control of neural brain rhythms
have been motivated by the advent of deep brain stimulation as a therapeutic treatment for a …

We explore the phase reduction in networks of coupled oscillators in the higher orders of the
coupling parameter. For coupled Stuart–Landau oscillators, where the phase can be …

While phase reduction is a tremendously useful tool for understanding the dynamics of
weakly perturbed limit cycle oscillators, its assumptions break down as perturbations …

An overview is given on two representative methods of dynamical reduction known as centre-
manifold reduction and phase reduction. These theories are presented in a somewhat more …