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 …

The coordinated development of multicellular organisms is driven by intercellular
communication. Differentiation into diverse cell types is usually associated with the …

Coupling delays may cause drastic changes in the dynamics of oscillatory networks. In the
present paper we investigate how coupling delays alter synchronization processes in …

Robust heteroclinic cycles occur naturally in many classes of nonlinear differential equations
with invariant hyperplanes. In particular they occur frequently in models for ecological …

Coupling of chaotic oscillators can lead to dynamical clustering where elements
spontaneously differentiate into groups of synchronized oscillators. When the clusters are …

A systematic and rigorous method to construct symplectic maps near separatrix of generic
Hamiltonian systems subjected to time-periodic perturbations is developed. It is based on …

One aim of synthetic biology is to construct increasingly complex genetic networks from
interconnected simpler ones to address challenges in medicine and biotechnology …

The present paper is the second part of a brief survey of development of the Kuramoto
model of coupled phase oscillators. We consider several systems obtained as …

Winnerless competition is analyzed in coupled maps with discrete temporal evolution of the
Lotka-Volterra type of arbitrary dimension. Necessary and sufficient conditions for the …

In this article we discuss, with a combination of analytical and numerical results, a canonical
set of differential equations with a robust heteroclinic cycle, subjected to time-periodic …