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We point out the existence of a transition from partial to global generalizedsynchronization (GS) in symmetrically coupled structurally different time-delaysystems of different orders using the auxiliary system approach and the mutualfalse nearest neighbor method. The present authors have recently reported thatthere exists a common GS manifold even in an ensemble of structurallynonidentical scalar time-delay systems with different fractal dimensions andshown that GS occurs simultaneously with phase synchronization (PS). In thispaper we confirm that the above result is not confined just to scalarone-dimensional time-delay systems alone but there exists a similar type oftransition even in the case of time-delay systems with different orders. Wecalculate the maximal transverse Lyapunov exponent to evaluate the asymptoticstability of the complete synchronization manifold of each of the main and thecorresponding auxiliary systems, which in turn ensures the stability of the GSmanifold between the main systems. Further we estimate the correlationcoefficient and the correlation of probability of recurrence to establish therelation between GS and PS. We also calculate the mutual false nearest neighborparameter which doubly confirms the occurrence of the global GS manifold.

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