  We investigate the stability of the synchronization manifold in a ring and an
open-ended chain of nearest neighbors coupled self-sustained systems, each
self-sustained system consisting of multi-limit cycles van der Pol oscillators.
Such model represents, for instance, coherent oscillations in biological
systems through the case of an enzymatic-substrate reaction with ferroelectric
behavior in brain waves model. The ring and open-ended chain of identical and
non-identical oscillators are considered separately. By using the Master
Stability Function approach (for the identical case) and the complex Kuramoto
order parameter (for the non-identical case), we derive the stability
boundaries of the synchronized manifold. We have found that synchronization
occurs in a system of many coupled modified van der Pol oscillators and it is
stable even in presence of a spread of parameters.
