We analyze a large system of nonlinear phase oscillators with sinusoidal nonlinearity,
uniformly distributed natural frequencies and global all-to-all coupling, which is an extension …

We present an approach based on Gronwall's inequalities for the asymptotic complete
phase–frequency synchronization of Kuramoto oscillators with finite inertia. For given finite …

We study a class of permutation-symmetric globally-coupled, phase oscillator networks on N-
dimensional tori. We focus on the effects of symmetry and of the forms of the coupling …

This paper formulates several algorithms for the direct computation of periodic orbits as
solutions of boundary value problems. The algorithms emphasize the use of coarse meshes …

We study synchronization in disordered arrays of Josephson junctions. In the first half of the
paper, we consider the relation between the coupled resistively and capacitively shunted …

We study the asymptotic complete entrainment of Kuramoto oscillators with inertia on
symmetric and connected network. We provide several sufficient conditions for the …

The Lindstedt--Poincaré technique in perturbation theory is used to calculate periodic orbits
of perturbed differential equations. It uses a nearby periodic orbit of the unperturbed …

Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours
under variation of the strength of the coupling. Network equations for pairs of coupled …

A system of ordinary differential equations (ODEs) is derived from a discrete system of
Vicsek, Czirók et al.[Phys. Rev. Lett. 75 (6): 1226–1229, 1995], describing the motion of a …

The continuation of periodic orbits is the main subject of this dissertation. However, our
contribution to the subject is divided into two main parts. In the first part, we focus on the …