Emergence of a common generalized synchronization manifold in network motifs of structurally different time-delay systems

• Published in: Chaos, solitons and fractals solitons and fractals, 2016-12, Vol.93, p.235-245
• Main Authors: Suresh, R., Senthilkumar, D.V., Lakshmanan, M., Kurths, J.
• Format: Article
• Language: English
• Subjects: Global generalized synchronization; Networks of time-delay systems; Partial generalized synchronization; Structurally different time-delay systems
• ISSN: 0960-0779; 1873-2887
• DOI: 10.1016/j.chaos.2016.10.016

•We have identified that a common generalized synchronization manifold exist for symmetrically coupled structurally different time-delay systems with different orders.•We have provided a theoretical formulation for the existence of a common generalized synchronization manifold based on the auxiliary system approach.•We have pointed out the existence of a transition from partial to global generalized synchronization.•We have corroborated our results using the maximal transverse Lyapunov exponent, correlation coefficient, mutual false nearest neighbor method. We point out the existence of a transition from partial to global generalized synchronization (GS) in symmetrically coupled structurally different time-delay systems of different orders using the auxiliary system approach and the mutual false nearest neighbor method. The present authors have recently reported that there exists a common GS manifold even in an ensemble of structurally nonidentical scalar time-delay systems with different fractal dimensions and shown that GS occurs simultaneously with phase synchronization (PS). In this paper we confirm that the above result is not confined just to scalar one-dimensional time-delay systems alone but there exists a similar type of transition even in the case of time-delay systems with different orders. We calculate the maximal transverse Lyapunov exponent to evaluate the asymptotic stability of the complete synchronization manifold of each of the main and the corresponding auxiliary systems, which in turn ensures the stability of the GS manifold between the main systems. Further we estimate the correlation coefficient and the correlation of probability of recurrence to establish the relation between GS and PS. We also calculate the mutual false nearest neighbor parameter which doubly confirms the occurrence of the global GS manifold.