Global and Partial Phase Synchronizations in Arrays of Piecewise Linear Time-Delay Systems

In this paper, we report the identification of global and partial phase synchronizations in linear arrays of unidirectionally coupled piecewise linear time-delay systems with two different coupling configurations. In particular, in a linear array with open end boundary conditions, global phase synchronization (GPS) is achieved by a sequential synchronization as a function of the coupling strength (a second order transition). Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. On the other hand, in a linear array with closed end boundary conditions (ring topology), partial phase synchronization (PPS) is achieved by forming different groups of phase synchronized clusters above some threshold value of the coupling strength (a first order transition) where they continue to be in a stable PPS state. We confirm the occurrence of both global and partial phase synchronizations in two different piecewise linear time-delay systems using various numerical methods.Comment: 26 pages, 25 figures, To Appear in International Journal of Bifurcation and Chaos, Vol. 22, No. 7 pp. 1250178 (1-25). arXiv admin note: substantial text overlap with arXiv:1007.280

Global generalized synchronization in networks of different time-delay systems

We show that global generalized synchronization (GS) exists in structurally different time-delay systems, even with different orders, with quite different fractal (Kaplan-Yorke) dimensions, which emerges via partial GS in symmetrically coupled regular networks. We find that there exists a smooth transformation in such systems, which maps them to a common GS manifold as corroborated by their maximal transverse Lyapunov exponent. In addition, an analytical stability condition using the Krasvoskii-Lyapunov theory is deduced. This phenomenon of GS in strongly distinct systems opens a new way for an effective control of pathological synchronous activity by means of extremely small perturbations to appropriate variables in the synchronization manifold.Comment: 6 pages, 4 figures, Accepted for publication in Europhys. Let

Global phase synchronization in an array of time-delay systems

We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.Comment: 11 pages, 13 figures, Appear in Physical Review

Zero-lag synchronization in coupled time-delayed piecewise linear electronic circuits

We investigate and report an experimental confirmation of zero-lag synchronization (ZLS) in a system of three coupled time-delayed piecewise linear electronic circuits via dynamical relaying with different coupling configurations, namely mutual and subsystem coupling configurations. We have observed that when there is a feedback between the central unit (relay unit) and at least one of the outer units, ZLS occurs in the two outer units whereas the central and outer units exhibit inverse phase synchronization (IPS). We find that in the case of mutual coupling configuration ZLS occurs both in periodic and hyperchaotic regimes, while in the subsystem coupling configuration it occurs only in the hyperchaotic regime. Snapshots of the time evolution of outer circuits as observed from the oscilloscope confirm the occurrence of ZLS experimentally. The quality of ZLS is numerically verified by correlation coefficient and similarity function measures. Further, the transition to ZLS is verified from the changes in the largest Lyapunov exponents and the correlation coefficient as a function of the coupling strength. IPS is experimentally confirmed using time series plots and also can be visualized using the concept of localized sets which are also corroborated by numerical simulations. In addition, we have calculated the correlation of probability of recurrence to quantify the phase coherence. We have also analytically derived a sufficient condition for the stability of ZLS using the Krasovskii-Lyapunov theory.Comment: 11 pages, 19 figures, Submitte

The leaf-feeding geometrid Isturgia disputaria (Guenee)-A potential biological control agent for prickly acacia, Vachellia nilotica subsp. indica (Benth.) Kyal. & Boatwr. (Mimosaceae) in Australia

Prickly acacia (Vachellia nilotica subsp. indica), a native multipurpose tree in India, is a weed of National significance, and a target for biological control in Australia. Based on plant genetic and climatic similarities, native range surveys for identifying potential biological control agents for prickly acacia were conducted in India during 2008-2011. In the survey leaf-feeding geometrid, Isturgia disputaria Guenee (syn. Tephrina pulinda), widespread in Tamil Nadu and Karnataka States, was prioritized as a potential biological control agent based on field host range, damage potential and no choice test on non target plant species. Though the field host range study exhibited that V. nilotica ssp. indica and V. nilotica ssp. tomentosa were the primary hosts for successful development of the insect, I. disputaria, replicated no - choice larval feeding and development tests conducted on cut foliage and live plants of nine non-target acacia test plant species in India revealed the larval feeding and development on three of the nine non-target acacia species, V. tortilis, V. planiferons and V. leucophloea in addition to the V. nilotica ssp. indica and V. nilotica ssp. tomentosa. However, the proportion of larvae developing into adults was higher on V. nilotica subsp. indica and V. nilotica subsp. tomentosa, with 90% and 80% of the larvae completing development, respectively. In contrast, the larval mortality was higher on V. tortilis (70%), V. leucophloea (90%) and V. planiferons (70%). The no-choice test results support the earlier host specificity test results of I. disputaria from Pakistan, Kenya and under quarantine in Australia. Contrasting results between field host range and host use pattern under no-choice conditions are discussed