Phase-flip Transition Research Articles

Phase-flip transition in volume-mismatched pairs of coupled 1-pentanol drops.

We have explored a variety of synchronization domains and observed phase-flip transition in a pair of coupled 1-pentanol drops as a function of the volume mismatch. Both experimental observations and numerical studies are presented. The experiments were carried out in a rectangular channel in a ferroin deionized water solution premixed with some volume of pentanol. A single pentanol drop (≥3μL) performs back and forth oscillations along the length of the channel due to the well-known Marangoni forces. In the present work, for a pair of drops, the drop 1 volume was changed from 3 to 5 μL in steps of 1μL, whereas the drop 2 volume was varied from 1 to 3 μL in steps of 0.5μL. A systematic investigation of all the possible combinations of the drop volumes showed the presence of three different types of synchrony-in-phase, antiphase, and phase-switched. In-phase synchronization was robust for a volume mismatch of >3.0μL between the two drops. On the other hand, antiphase synchronization was robust when the volume mismatch was <2.0μL. The phase-switched state is a synchronized state involving a phase-flip transition in the time domain. This state was observed for the intermediate range of volume mismatch. Numerically, the system has been investigated using two Stuart-Landau oscillators interacting via a coupling function in the form of Lennard-Jones potential. The numerical results suitably capture both in-phase and antiphase oscillations for a pair of volume-mismatched pentanol drops.

Time delay induced partial death patterns with conjugate coupling in relay oscillators

We investigate the dynamics of delay-coupled relay oscillators with conjugate (or dissimilar) coupling and find the partial death with the phase-flip transition. This phenomenon is quite general and occurs for the limit cycle as well as chaotic relay oscillators. In the regime of partial death, parts of the system oscillate with large amplitude, while other element stays at rest. Using the Stuart-Landau and Rössler oscillators, we demonstrate that partial amplitude death is a robust dynamical state in coupled oscillators. We also studied the mismatch delay and find different types of dynamical pattern with partial death.

Phase-flip in relay oscillators via linear augmentation

In time-delay coupled relay system of three limit cycle of oscillators, linear augmentation control provides an effective strategy to induce phase-flip from relative phase zero to π between spatially separated oscillators. A coexisting dynamical regime of fixed point and anti-phase synchronization state is harnessed in relay system. Targeting phase-flip transition through linear augmentation is illustrated by using Stuart-Landau oscillators. However, such dynamical transition does not occur in the same system with conjugate coupling through dissimilar variables. Inducing relative phase difference without resorting to variation of internal system parameters and time-delay is important from the view of system control.

Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators

A complex collective emerging behavior characterized by coexisting coherent and incoherent domains is termed as a chimera state. We bring out the existence of a new type of chimera in a nonlocally coupled ensemble of identical oscillators driven by a common dynamic environment. The latter facilitates the onset of phase-flip bifurcation/transitions among the coupled oscillators of the ensemble, while the nonlocal coupling induces a partial asynchronization among the out-of-phase synchronized oscillators at this onset. This leads to the manifestation of coexisting out-of-phase synchronized coherent domains interspersed by asynchronous incoherent domains elucidating the existence of a different type of chimera state. In addition to this, a rich variety of other collective behaviors such as clusters with phase-flip transition, conventional chimera, solitary state and complete synchronized state which have been reported using different coupling architectures are found to be induced by the employed couplings for appropriate coupling strengths. The robustness of the resulting dynamics is demonstrated in ensembles of two paradigmatic models, namely Rössler oscillators and Stuart-Landau oscillators.

External control of the synchronization dynamics of two inductively coupled glow discharge plasma sources

An experimental investigation of the influence of an external periodic forcing on the synchronization dynamics of two inductively coupled plasma sources is reported. The driven response of the coupled system is found to have a rich structure in the parameter space of the frequency and the amplitude of the external driver. In particular, there is a strong impact on the nature of the phase-flip transitions between anti-phase and in-phase synchronized states of the system and the frequency bifurcation structure of the collective states. The external driver provides a convenient tool for accessing various collective states of the system and controlling the collective dynamics of the two coupled systems through a proper choice of its frequency and amplitude. Our experimental results are qualitatively supported by numerical simulation results from a theoretical model of two environmentally coupled van der Pol equations, one of which is also driven externally.

Phase-flip and oscillation-quenching-state transitions through environmental diffusive coupling.

We study the dynamics of nonlinear oscillators coupled through environmental diffusive coupling. The interaction between the dynamical systems is maintained through its agents which, in turn, interact globally with each other in the common dynamical environment. We show that this form of coupling scheme can induce an important transition like phase-flip transition as well transitions among oscillation quenching states in identical limit-cycle oscillators. This behavior is analyzed in the parameter plane by analytical and numerical studies of specific cases of the Stuart-Landau oscillator and van der Pol oscillator. Experimental evidences of the phase-flip transition and quenching states are shown using an electronic version of the van der Pol oscillators.

Experimental observation of phase-flip transitions in two inductively coupled glow discharge plasmas.

We report an experimental observation of a phase-flip transition in the frequency synchronization of two dc glow discharge plasma sources that are coupled in a noninvasive fashion. When the fundamental oscillation frequency of the potential fluctuations of one of the sources is progressively increased, by raising its discharge voltage, a frequency pulling regime is observed, followed by a synchronized regime that shows a frequency jump phenomenon. The jump is associated with a phase-flip transition that takes the synchronized state from an in-phase to an antiphase state. When the process is reversed, the transition takes place at a different frequency, thereby exhibiting a hysteresis effect. A heuristic model, consisting of two van der Pol oscillators that are coupled to each other through a dynamic common medium, eminently captures the essential features of our experimental observations.

Experimental observation of phase-flip transitions in the brain.

The phase-flip transition has been demonstrated in a host of coupled nonlinear oscillator models, many pertaining directly to understanding neural dynamics. However, there is little evidence that this phenomenon occurs in the brain. Using simultaneous microelectrode recordings in the nonhuman primate cerebral cortex, we demonstrate the presence of phase-flip transitions between oscillatory narrow-band local field potential signals separated by several centimeters. Specifically, we show that sharp transitions between in-phase and antiphase synchronization are accompanied by a jump in synchronization frequency. These findings are significant for two reasons. First, they validate predictions made by model systems. Second, they have potentially far reaching implications for our understanding of the mechanisms underlying corticocortical communication, which are thought to rely on narrow-band oscillatory synchronization with specific relative phase relationships.

Dynamics of Attractively and Repulsively Coupled Elementary Chaotic Systems

We investigate an elementary model for doubly coupled dynamical systems that consists of two identical, mutually interacting minimal chaotic flows in the form of jerky dynamics. The coupling mechanisms allow for the simultaneous presence of attractive and repulsive interactions between the systems. Despite its functional simplicity, the model is capable of exhibiting diverse types of dynamical phenomena induced by the presence of the couplings. We provide an in-depth numerical investigation of the dynamics depending on the coupling strengths and the autonomous dynamical behavior of the subsystems. Partly, the dynamics of the system can be analytically understood using the Poincaré–Lindstedt method. An approximation of periodic orbits is carried out in the vicinity of a phase-flip transition that leads to deeper insights into the organization of the appearing dynamics in the parameter space. In addition, we propose a circuit that enables an electronic implementation of the model. A variation of the coupling mechanism to a coupling in conjugate variables leads to a regime of amplitude death.

Effects of Couplings on the Collective Dynamics of Permanent-Magnet Synchronous Motors

Recently, researchers have reported that couplings play a crucial role in determining important evolutions of nonlinear systems. In this paper, the collective dynamics of two coupled permanent-magnet synchronous motors (PMSMs) are investigated, and it is found that with positive and negative couplings, the coupled PMSMs display rich phenomena, such as complete synchronization, amplitude death (AD), antiphase synchronization, phase-flip transition, and so on. Among these collective behaviors, AD, which is of considerable importance in maintaining the secure and stable operation of coupled PMSMs, is extensively studied. The relationship among various dynamics and transitions to AD is also illustrated.

Observation of phase-flip transition in delay-coupled Nishio-Inaba circuits

We examine the dynamics of two time-delay coupled Nishio-Inaba circuits exhibiting limit-cycle motion. By numerically solving the governing delay-differential equations, we show that the delay coupled Nishio-Inaba circuits undergo a phase-flip transition. Our results reveal that depending on the strength of coupling and the amount of time-delay, the relative phase between the oscillators changes from in-phase to anti-phase and vice versa, and the pattern repeats with increasing delay. We also verify our numerical predictions using OrCAD PSpice circuit simulation.

Phase-flip transition in nonlinear oscillators coupled by dynamic environment

We study the dynamics of nonlinear oscillators indirectly coupled through a dynamical environment or a common medium. We observed that this form of indirect coupling leads to synchronization and phase-flip transition in periodic as well as chaotic regime of oscillators. The phase-flip transition from in- to anti-phase synchronization or vise-versa is analyzed in the parameter plane with examples of Landau-Stuart and Rössler oscillators. The dynamical transitions are characterized using various indices such as average phase difference, frequency, and Lyapunov exponents. Experimental evidence of the phase-flip transition is shown using an electronic version of the van der Pol oscillators.

Frequency discontinuity and amplitude death with time-delay asymmetry

We consider oscillators coupled with asymmetric time delays, namely, when the speed of information transfer is direction dependent. As the coupling parameter is varied, there is a regime of amplitude death within which there is a phase-flip transition. At this transition the frequency changes discontinuously, but unlike the equal delay case when the relative phase difference changes by π, here the phase difference changes by an arbitrary value that depends on the difference in delays. We consider asymmetric delays in coupled Landau-Stuart oscillators and Rössler oscillators. Analytical estimates of phase synchronization frequencies and phase differences are obtained by separating the evolution equations into phase and amplitude components. Eigenvalues and eigenvectors of the Jacobian matrix in the neighborhood of the transition also show an "avoided crossing," as has been observed in previous studies with symmetric delays.

Phase-flip transition in relay-coupled nonlinear oscillators

We study the dynamics of oscillators that are coupled in relay; namely, through an intermediary oscillator. From previous studies it is known that the oscillators show a transition from in-phase to out-of-phase oscillations or vice versa when the interactions involve a time delay. Here we show that, in the absence of time delay, relay coupling through conjugate variables has the same effect. However, this phase-flip transition does not occur abruptly at a certain critical value of the coupling parameter. Instead we find a parameter region around the phase-flip transition where bistability occurs. In this parameter interval in-phase and out-of-phase oscillations coexist with changing sizes of their basins of attraction. Further increase of the coupling strength leads to amplitude death and subsequently to the stabilization of a fixed point. These transitions are characterized through various quantities such as the average phase difference and crossings in the spectrum of Lyapunov exponents. Numerical results are presented for a specific case of coupled Rössler-like oscillators.

Time-delay-induced phase-transition to synchrony in coupled bursting neurons

Signal transmission time delays in a network of nonlinear oscillators are known to be responsible for a variety of interesting dynamic behaviors including phase-flip transitions leading to synchrony or out of synchrony. Here, we uncover that phase-flip transitions are general phenomena and can occur in a network of coupled bursting neurons with a variety of coupling types. The transitions are marked by nonlinear changes in both temporal and phase-space characteristics of the coupled system. We demonstrate these phase-transitions with Hindmarsh-Rose and Leech-Heart interneuron models and discuss the implications of these results in understanding collective dynamics of bursting neurons in the brain.

Nature of the phase-flip transition in the synchronized approach to amplitude death

We study the dynamics of time-delay coupled limit-cycle oscillators in the amplitude death regime. Through a detailed analysis of the Jacobian at the fixed point, we show that the phase-flip transition, namely, the abrupt change from in-phase synchronized dynamics to antiphase synchronized dynamics, is associated with an interchange of the imaginary parts of complex pairs of eigenvalues at an "avoided crossing" of Lyapunov exponents as a parameter is varied. An order parameter for the transition is constructed through the eigenvectors of the Jacobian.

Phase-flip transition in coupled electrochemical cells

Time delay is introduced in the coupling between a pair of electrochemical cells. As coupling parameters are varied, the anodic current in the two cells oscillate in synchrony in regimes of periodic as well as chaotic dynamics. When the time delay is varied a phase-flip transition is observed: the relative phase between the synchronized oscillations changes abruptly by pi . This is accompanied by an experimentally measurable discontinuous change in the frequency of the synchronized oscillators.

Fluctuational phase-flip transitions in parametrically driven oscillators

We analyze the rates of noise-induced transitions between period-two attractors. The model investigated is an underdamped oscillator parametrically driven by a field at nearly twice the oscillator eigenfrequency. The activation energy of the transitions is analyzed as a function of frequency detuning and field amplitude scaled by the damping and nonlinearity parameters of the oscillator. Both fourth- and sixth-order nonlinearities are taken into account. The parameter ranges where the system is bistable and tristable are investigated. Explicit results are obtained in the limit of small damping, or equivalently, strong driving, including scaling near bifurcation points.