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

Abstract

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. * Electronic address:

Generalized Synchronization Between ENSO and Hydrological Variables in Colombia: A Recurrence Quantification Approach

“…Recently, RQA has proved to be useful in diverse areas, such as economy, physiology, earth sciences, astrophysics, and engineering [10,22]. In particular, RQA has been used to investigate complex synchronization scenarios between coupled chaotic oscillators [24], emergence of GS in networks of structurally different timedelay systems [25,26], and precursors and synchronization of components of the tectonic system [27], among others. The oscillatory nature of diverse hydroclimate phenomena is wellknown, such as those associated with the annual cycle of insolation (12 months), and the quasi-periodic El Niño-Southern Oscillation (3-4 years), which constitutes the most important modulator of interannual climate variability worldwide [28].…”

Bistability in network motifs of Duffing oscillators

“…Significantly less attention was paid to synchronization in network motifs of coupled oscillators. In this respect, it is worth mentioning interesting studies with Rössler [Kapitaniak et al, 2015], Rulkov [Sausedo-Solorio and Pisarchik, 2017;Pisarchik et al, 2019], Stuart-Landau [Karakaya et al, 2019], Hodgkin-Huxley [Mirasso et al, 2017], and other models [Suresh et al, 2016]. Concerning Duffing oscillators, we have to mention the paper of Jaros et al [Jaros et al, 2016], who observed different bifurcation scenarios with respect to the coupling strength in three unidirectionally coupled Duffing oscillators. In this paper, we study dynamics of simplest network motifs formed by three Duffing oscillators.…”