An important aspect of the recently introduced transient uncoupling scheme is that it induces synchronization for large values of coupling strength at which the coupled chaotic systems resist synchronization when continuously coupled. However, why this is so is an open problem? To answer this question, we recall the conventional wisdom that the eigenvalues of the Jacobian of the transverse dynamics measure whether a trajectory at a phase point is locally contracting or diverging with respect to another nearby trajectory. Subsequently, we go on to highlight a lesser appreciated fact that even when, under the corresponding linearised flow, the nearby trajectory asymptotically diverges away, its distance from the reference trajectory may still be contracting for some intermediate period. We term this phenomenon transient decay in line with the phenomenon of the transient growth. Using these facts, we show that an optimal coupling region, i.e., a region of the phase space where coupling is on, should ideally be such that at any of the constituent phase point either the maximum of the real parts of the eigenvalues is negative or the magnitude of the positive maximum is lesser than that of the negative minimum. We also invent and employ a modified dynamics coupling scheme-a significant improvement over the well-known dynamic coupling scheme-as a decisive tool to justify our results.

Owing to the absence of the phase space attractors in the Hamiltonian dynamical systems, the concept of the identical synchronization between the dissipative systems is inapplicable to the Hamiltonian systems for which, thus, one defines a related generalized phenomenon known as the measure synchronization. A coupled pair of Hamiltonian systems-the full coupled system also being Hamiltonian-can possibly be in two types of measure synchronized states: quasiperiodic and chaotic. In this paper, we take representative systems belonging to each such class of the coupled systems and highlight that, as the coupling strengths are varied, there may exist intervals in the ranges of the coupling parameters at which the systems are measure desynchronized. Subsequently, we illustrate that as a coupled system evolves in time, occasionally switching off the coupling when the system is in the measure desynchronized state can bring the system back in measure synchrony. Furthermore, for the case of the occasional uncoupling being employed periodically and the corresponding time-period being small, we analytically find the values of the on-fraction of the time-period during which measure synchronization is effected on the corresponding desynchronized state.

Measure synchronization is a well-known phenomenon in coupled classical Hamiltonian systems over last two decades. In this paper, synchronization for coupled Harper system is investigated in both classical and quantum contexts. The concept of measure synchronization involves with the phase space and it seems that the measure synchronization is restricted in classical limit. But, on the contrary, here, we have extended the aforesaid synchronization in quantum domain. In quantum context, the coupling occurs between two many body systems via a time and site dependent potential. The coupling leads to the generation of entanglement between the quantum systems. We have used a technique, which is already accepted in the classical domain, in both the contexts to establish a connection between classical and quantum scenarios. Interestingly, results corresponding to both the cases lead to some common features. (Saikat Sur), anupamgh@iitk.ac.in (Anupam Ghosh) not observed. Also, since the Hamiltonian systems follow the Liouville's theorem, there is no existence of attractor here unlike the dissipative systems. Therefore, one would get a different type of synchronization: 'measure synchronization' (MS), in coupled Hamiltonian systems, reported in 1999 (Hampton andZanette, 1999).

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Synchronization in coupled dynamical systems has been a well-known phenomenon in the field of nonlinear dynamics for a long time. This phenomenon has been investigated extensively both analytically and experimentally. Although synchronization is observed in different areas of our real life, in some cases, this phenomenon is harmful; consequently, an early warning of synchronization becomes an unavoidable requirement. This paper focuses on this issue and proposes a reliable measure ([Formula: see text]), from the perspective of the information theory, to detect complete and generalized synchronizations early in the context of interacting oscillators. The proposed measure [Formula: see text] is an explicit function of the joint entropy and mutual information of the coupled oscillators. The applicability of [Formula: see text] to anticipate generalized and complete synchronizations is justified using numerical analysis of mathematical models and experimental data. Mathematical models involve the interaction of two low-dimensional, autonomous, chaotic oscillators and a network of coupled Rössler and van der Pol oscillators. The experimental data are generated from laboratory-scale turbulent thermoacoustic systems.

In this paper, we critically reexplore the stochastic and the deterministic occasional uncoupling methods of effecting identical synchronized states in low dimensional, dissipative, diffusively coupled, chaotic flows that are otherwise not synchronized when continuously coupled at the same coupling strength parameter. In the process of our attempt to understand the mechanisms behind the success of the occasional uncoupling schemes, we devise a hybrid between the transient uncoupling and the stochastic on-off coupling, and aptly name it the transient stochastic uncoupling-yet another stochastic occasional uncoupling method. Our subsequent investigation on the transient stochastic uncoupling allows us to surpass the effectiveness of the stochastic on-off coupling with very fast on-off switching rate. Additionally, through the transient stochastic uncoupling, we establish that the indicators quantifying the local contracting dynamics in the corresponding transverse manifold are generally not useful in finding the optimal coupling region of the phase space in the case of the deterministic transient uncoupling. In fact, we highlight that the autocorrelation function-a non-local indicator of the dynamics-of the corresponding response system's chaotic time-series dictates when the deterministic uncoupling could be successful.

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This paper aims to study amplitude death in time delay coupled oscillators using the occasional coupling scheme that implies intermittent interaction among the oscillators. An enhancement of amplitude death regions (i.e., an increment of the width of the amplitude death regions along the control parameter axis) can be possible using the occasional coupling in a pair of delay-coupled oscillators. Our study starts with coupled limit cycle oscillators (Stuart–Landau) and coupled chaotic oscillators (Rössler). We further examine coupled horizontal Rijke tubes, a prototypical model of thermoacoustic systems. Oscillatory states are highly detrimental to thermoacoustic systems such as combustors. Consequently, a state of amplitude death is always preferred. We employ the on–off coupling (i.e., a square wave function), as an occasional coupling scheme, to these coupled oscillators. On monotonically varying the coupling strength (as a control parameter), we observe an enhancement of amplitude death regions using the occasional coupling scheme compared to the continuous coupling scheme. In order to study the contribution of the occasional coupling scheme, we perform a detailed linear stability analysis and analytically explain this enhancement of the amplitude death region for coupled limit cycle oscillators. We also adopt the frequency ratio of the oscillators and the time delay between the oscillators as the control parameters. Intriguingly, we obtain a similar enhancement of the amplitude death regions using the frequency ratio and time delay as the control parameters in the presence of the occasional coupling. Finally, we use a half-wave rectified sinusoidal wave function (motivated by practical reality) to introduce the occasional coupling in time delay coupled oscillators and get similar results.