Transition from anticipatory to lag synchronization via complete synchronization in time-delay systems

The existence of anticipatory, complete and lag synchronization in a single system having two different time-delays, that is feedback delay $\tau_1$ and coupling delay $\tau_2$, is identified. The transition from anticipatory to complete synchronization and from complete to lag synchronization as a function of coupling delay $\tau_2$ with suitable stability condition is discussed. The existence of anticipatory and lag synchronization is characterized both by the minimum of similarity function and the transition from on-off intermittency to periodic structure in laminar phase distribution.Comment: 14 Pages and 12 Figure

Phase synchronization in time-delay systems

Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In this article we report the first identification of phase synchronization in coupled time-delay systems exhibiting hyperchaotic attractor. We show that there is a transition from non-synchronized behavior to phase and then to generalized synchronization as a function of coupling strength. These transitions are characterized by recurrence quantification analysis, by phase differences based on a new transformation of the attractors and also by the changes in the Lyapunov exponents. We have found these transitions in coupled piece-wise linear and in Mackey-Glass time-delay systems.Comment: 4 pages, 3 Figures (To appear in Physical Review E Rapid Communication

Motion of Curves and Surfaces and Nonlinear Evolution Equations in (2+1) Dimensions

It is shown that a class of important integrable nonlinear evolution equations in (2+1) dimensions can be associated with the motion of space curves endowed with an extra spatial variable or equivalently, moving surfaces. Geometrical invariants then define topological conserved quantities. Underlying evolution equations are shown to be associated with a triad of linear equations. Our examples include Ishimori equation and Myrzakulov equations which are shown to be geometrically equivalent to Davey-Stewartson and Zakharov -Strachan (2+1) dimensional nonlinear Schr\"odinger equations respectively.Comment: 13 pages, RevTeX, to appear in J. Math. Phy

Wheat Growth, Yield, and Yield Contributing Attributes as a Function of Nitrogen Levels

To evaluate the effect of different levels of nitrogen on growth and yield of wheat a field experiment was conducted in 2017-18 at research area of cereals and pulses section, Ayyub agricultural research institute, Faisalabad. Eight levels of nitrogen i.e. 0, 29, 58, 87, 116, 145, 174, 203 kg ha-1 were evaluated. Experiment was laid out under randomized complete block design (RCBD) with three replications with a net plot size of 10×5m. Data were recorded for growth and yield parameters like number of tillers, plant height, spiklets per spike, seeds per spike, biological yield, 1000 grain weight, grain yield and harvest index. Different levels of nitrogen significantly increased all the growth and yield parameters. Maximum number of tillers, highest plant height and biological yield was recorded from the treatment where nitrogen was applied @ 203 Kg ha-1 while 1000 grain yield, seeds per spike and grain yield was achieved highest from where nitrogen applied @ 145 Kg ha-1

Experimental confirmation of chaotic phase synchronization in coupled time-delayed electronic circuits

We report the first experimental demonstration of chaotic phase synchronization (CPS) in unidirectionally coupled time-delay systems using electronic circuits. We have also implemented experimentally an efficient methodology for characterizing CPS, namely the localized sets. Snapshots of the evolution of coupled systems and the sets as observed from the oscilloscope confirming CPS are shown experimentally. Numerical results from different approaches, namely phase differences, localized sets, changes in the largest Lyapunov exponents and the correlation of probability of recurrence ($C_{CPR}$), corroborate the experimental observations.Comment: Physical_Review_E_82_065201(R) 201

Transition from phase to generalized synchronization in time-delay systems

The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the identification of phase synchronization in coupled nonidentical piece-wise linear and in coupled Mackey-Glass time-delay systems with highly non-phase-coherent regimes. We show that there is a transition from non-synchronized behavior to phase and then to generalized synchronization as a function of coupling strength. We have introduced a transformation to capture the phase of the non-phase coherent attractors, which works equally well for both the time-delay systems. The instantaneous phases of the above coupled systems calculated from the transformed attractors satisfy both the phase and mean frequency locking conditions. These transitions are also characterized in terms of recurrence based indices, namely generalized autocorrelation function $P(t)$, correlation of probability of recurrence (CPR), joint probability of recurrence (JPR) and similarity of probability of recurrence (SPR). We have quantified the different synchronization regimes in terms of these indices. The existence of phase synchronization is also characterized by typical transitions in the Lyapunov exponents of the coupled time-delay systems.Comment: Accepted for publication in CHAO

Quantitative Precipitation Nowcasting: A Lagrangian Pixel-Based Approach

Short-term high-resolution precipitation forecasting has important implications for navigation, flood forecasting, and other hydrological and meteorological concerns. This article introduces a pixel-based algorithm for Short-term Quantitative Precipitation Forecasting (SQPF) using radar-based rainfall data. The proposed algorithm called Pixel- Based Nowcasting (PBN) tracks severe storms with a hierarchical mesh-tracking algorithm to capture storm advection in space and time at high resolution from radar imagers. The extracted advection field is then extended to nowcast the rainfall field in the next 3. hr based on a pixel-based Lagrangian dynamic model. The proposed algorithm is compared with two other nowcasting algorithms (WCN: Watershed-Clustering Nowcasting and PER: PERsistency) for ten thunderstorm events over the conterminous United States. Object-based verification metric and traditional statistics have been used to evaluate the performance of the proposed algorithm. It is shown that the proposed algorithm is superior over comparison algorithms and is effective in tracking and predicting severe storm events for the next few hours. © 2012 Elsevier B.V

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