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 …

Today, based on brain imaging analyses, we can consider the brilliant metaphor about
event discreteness of the conscious process by William James (1890) to be an experimental …

Pattern formation in physical systems is one of the major research frontiers of mathematics.
A central theme of this book is that many instances of pattern formation can be understood …

We show that series arrays of N identical overdamped Josephson junctions have extremely
degenerate dynamics. In particular, we prove that such arrays have N− 3 constants of motion …

This book deals with the bifurcation and chaotic aspects of damped and driven nonlinear
oscillators. The analytical and numerical aspects of the chaotic dynamics of these oscillators …

Animal locomotion typically employs several distinct periodic patterns of leg movements,
known as gaits. It has long been observed that most gaits possess a degree of symmetry …

We show that a dynamical system of N phase oscillators with global cosine coupling is
completely integrable. In particular, we prove that the N-dimensional phase space is foliated …

We present a framework for analysing arbitrary networks of identical dissipative oscillators
assuming weak coupling. Using the symmetry of the network, we find dynamically invariant …

We investigate the phenomenon of chaos synchronization and efficient signal transmission
in a physically interesting model, namely, the Van der Pol–Duffing oscillator. A criterion for …

Microresonators are micron-scale optical systems that confine light using total internal
reflection. These optical systems have gained interest in the past two decades due to their …