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

Abstract

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 R. Yamapi ( ) 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.

Bifurcation, amplitude death and oscillation patterns in a system of three coupled van der Pol oscillators with diffusively delayed velocity coupling

“…Using the decomposition u t ¼ UxðtÞ þ y; with xðtÞ 2 C p and y 2 Q 1 Q \ C 1 (C 1 is the subset of C consisting of continuously differentiable functions). Then we can decompose (17) as…”

“…In Ref. 17, 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 multilimit cycle van der Pol oscillators, has been investigated and it has been 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.…”

Modulation of synchronization dynamics in a network of self-sustained systems

“…Recently, these results have been validated experimentally and the consequences of parameter mismatch have been also emphasized [17]. But, these studies [16,17] and others [18][19][20] have considered only the influence of nearest neighbors coupling on stability boundaries using both analytical and numerical investigations. Thus, we want to investigate in this paper the modulatory effect of non-nearest neighbors and the local injection on synchronized states and their corresponding stability boundaries.…”

Synchronization enhancement via an oscillatory bath in a network of self-excited cells

“…[14]. The benefits of synchronization do not lie only in those situations where it can be found or explained in nature, but also in possible technological applications such as communication engineering, biology, chemistry and so on [15][16][17][18][19][20][21][22][23][24].…”