Stability of the synchronization manifold in nearest neighbor nonidentical van der Pol-like oscillators

We investigate the stability of the synchronization manifold in a ring and in an open-ended chain of nearest neighbor coupled self-sustained systems, each self-sustained system consisting of multi-limit cycle van der Pol oscillators. Such a model represents, for instance, coherent oscillations in biological systems through the case of an enzymatic-substrate reaction with ferroelectric behavior in a brain waves model. The ring and open-ended chain of identical and nonidentical oscillators are considered separately. By using the Master Stability Function approach (for the identical case) and the complex Kuramoto order parameter (for the nonidentical 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 the presence of a spread of parameters.