Anti-phase Synchronization Research Articles

Synchronization of a dual-exciter coupling with a torsion spring in far-resonance system

In-phase self-synchronization of two eccentric rotors with common rotational axis is hardly implemented in far-resonance system. In this article, a dual motor coaxially coupling with a torsion spring is proposed to obtain in-phase synchronization between the eccentric rotors. To explore the dynamic and synchronous characteristics of the proposed system, the mechanical model is first established with Lagrangian formulation. Second, the steady response of the system is calculated based on differential motion equations. Subsequently, the synchronous mechanism between the eccentric rotors is discussed by averaged small parameter method. Finally, some numerical computations are further implemented to verify correctness of theoretical analysis. The result shows that the synchronous state is determined by stiffness of torsion spring, masses of eccentric rotors, and distance between the motors. When axial distance between the motor is smaller, “critical stiffness of in-phase synchronization” is gradually enlarged as the masses of the eccentric rotors are increased and approached to equality, but in-phase synchronization is permanently maintained when the axial distance of the motor is far; in this situation, the synchronous state is hardly affected by variation of stiffness of torsion spring and masses of eccentric rotors. When the stiffness of the torsion spring is smaller, “critical distance [Formula: see text] of in-phase synchronization” is also enlarged as the masses of the eccentric rotors are increased and approached to equality; otherwise, the synchronous state is always locked in in-phase synchronization. When the stiffness of the torsion spring is smaller, “critical distance [Formula: see text] of anti-phase synchronization” is decreased as the masses of eccentric rotors are increased and approached to equality; otherwise, the synchronous state is always locked in in-phase synchronization.

Stochastic deformations of coupling-induced oscillatory regimes in a system of two logistic maps

We consider a system of two coupled identical logistic maps, which in isolation demonstrate stable equilibrium modes. Under increasing coupling strength, this system exhibits transitions from initial equilibrium regime to synchronized oscillatory behavior with complex modes, both regular (periodic or quasiperiodic) and chaotic. Moreover, the coupled subsystem can demonstrate synchronization with anti-phase oscillations in tonic or burst form. A novelty of this paper is related to analysis of noise-induced deformations of these corporative oscillatory regimes. For this model, the following constructive stochastic effects are studied: (i) noise-induced temporal destruction of the anti-phase synchronization with transition from tonic to burst oscillations, (ii) noise-induced destruction of 2-torus with the transition from quasiperiodic oscillations to the bursting, (iii) stochastic transformations of burst oscillations from regular to chaotic. An important role of transients and “riddled” basins in the study of stochastic shifts of crisis bifurcation points is discussed. For the analytical investigation of these phenomena, a method based on the stochastic sensitivity of attractors (discrete cycles and tori) and confidence domains is applied.

Synchronization in optically trapped polariton Stuart-Landau networks

We demonstrate tunable dissipative interactions between optically trapped exciton-polariton condensates. We apply annular shaped nonresonant optical beams to both generate and confine each condensate to their respective traps, pinning their natural frequencies. Coupling between condensates is realized through the finite escape rate of coherent polaritons from the traps leading to robust phase locking with neighboring condensates. The coupling is controlled by adjusting the polariton propagation distance between neighbors. This permits us to map out regimes of both strong and weak dissipative coupling, with the former characterized by clear in-phase and anti-phase synchronization of the condensates. With robust single-energy occupation governed by dissipative coupling of optically-trapped polariton condensates, we present a system which offers a potential optical platform for the optimization of randomly connected $XY$ Hamiltonians.

The Phenomenon of Bistable Phase Difference Intervals in the Times-Frequency Vibration Synchronization System Driven by Two Homodromy Exciters

A vibration system with two homodromy exciters operated in different rotational speed is established to investigate whether the phenomenon of bistable phase difference intervals exists in the times-frequency vibration synchronization system. Some constructive conclusions are proposed. (1) By introducing an average angular velocity perturbation parameter ε0 and two sets of phase difference perturbation parameters and ε2, the frequency capture criterion and the necessary criteria for realizing the times-frequency vibration synchronization are derived. The corresponding stability analysis is carried out. (2) By the theoretical analysis and experiments, it is verified that the times-frequency vibration synchronization system exists the phenomena of bistable phase difference interval. That is, the phase differences between the two homodromy exciters are stable around 180 degrees when they are located at a short distance; the antiphase synchronization phenomenon appears. On the contrary, they are stable around 0 degrees at the in-phase synchronization state. (3) Because of the two homodromy exciters operating in the different rotational speed, the vibration system obtains relatively complex compound motion trajectories; the corresponding application is investigated by adding a feeding material chamber. The times-frequency vibration synchronization system can be used to design the vibration mill for reducing its low-energy zone and developing chaotic mixing equipment for obtaining a better mixing effect.

Delay-Enhanced Synchronization in Two Coupled Chaotic Light-Emitting Diodes

In a light-emitting diode (LED) with ac-coupled nonlinear optoelectronic feedback, chaos can occur within a wide range of the voltage threshold parameter. When two identical such LEDs are coupled without delays, with increase of the coupling strength, transitions occur from anti-phase synchronization of periodic spiking to complete synchronization of chaos. Here we present that a coupling time-delay enhances chaos synchronization with small coupling strengths. The numerical simulations with bifurcation diagrams demonstrate the underlying mechanisms.

Delay-induced synchronization in two coupled chaotic memristive Hopfield neural networks

Abstract This paper is concerned with the synchronization of two coupled hyperbolic-type Hopfield neural networks with a memristive synaptic connection. The results show that the coupling with no time-delay cannot lead to complete synchronization and increasing the coupling strength causes anti-phase synchronization. While adding time-delays to the coupling term not only changes the dynamical behavior of the network but also facilitates reaching the full synchronization manifold. The network is investigated in two different cases of single and multiple time-delays. The calculated average‌ synchronization error indicates that using two time-delays has a better effect on the synchronization of systems. However, the synchronization region is lessened by increasing the time-delay values.

Membrane Structure Drives Synchronization Patterns in Arrays of Diffusively Coupled Self-Oscillating Droplets.

Networks of diffusively coupled inorganic oscillators, confined in nano- and microcompartments, are effective for predicting and understanding the global dynamics of those systems where the diffusion of activatory or inhibitory signals regulates the communication among different individuals. By taking advantage of a microfluidic device, we study the dynamics of arrays of diffusively coupled Belousov-Zhabotinsky (BZ) oscillators encapsulated in water-in-oil single emulsions. New synchronization patterns are induced and controlled by modulating the structural and chemical properties of the phospholipid-based biomimetic membranes via the introduction of specific dopants. Doping molecules do not alter the membrane basic backbone, but modify the lamellarity (and, in turn, the permeability) or interact chemically with the reaction intermediates. A transition from two-period clusters showing 1:2 period-locking to one-period antiphase synchronization is observed by decreasing the membrane lamellarity. An unsynchronized scenario is found when the dopant is able to interfere with chemical communication by reacting with the chemical messengers.

Effect of repulsive links on frustration in attractively coupled networks.

We investigate the impact of attractive-repulsive interaction in networks of limit cycle oscillators. Mainly we focus on the design principle for generating an antiphase state between adjacent nodes in a complex network. We establish that a partial negative control throughout the branches of a spanning tree inside the positively coupled limit cycle oscillators works efficiently well in comparison with randomly chosen negative links to establish zero frustration (antiphase synchronization) in bipartite graphs. Based on the emergence of zero frustration, we develop a universal 0-π rule to understand the antiphase synchronization in a bipartite graph. Further, this rule is used to construct a nonbipartite graph for a given nonzero frustrated value. We finally show the generality of 0-π rule by implementing it in arbitrary undirected nonbipartite graphs of attractive-repulsively coupled limit cycle oscillators and successfully calculate the nonzero frustration value, which matches with numerical data. The validation of the rule is checked through the bifurcation analysis of small networks. Our work may unveil the underlying mechanism of several synchronization phenomena that exist in a network of oscillators having a mixed type of coupling.

Antiphase synchronization and central symmetrical antiphase synchronization in magnetic field coupled circuits

The dynamics of memristor-based RLC circuit is explored on the effects of magnetic field coupling through a transformer in the circuit. With the increasing strength of magnetic field coupling, the two coupled RLC circuits firstly break the reflectional symmetry by transiting from double-scroll attractors to single-scroll attractors and then break the translational symmetry with two attractors in different sizes and shapes. The two single-scroll attractors are locked in antiphase synchronous states for positive magnetic field coupling while transit to a new kind of dynamic regime, named as central symmetrical antiphase synchronization (CSAS) for negative magnetic field coupling. Moreover, the single-scroll attractors in inphase synchronization or in CSAS may coexist with asynchronous states in some interval of coupling strength. The dynamics of the anti-synchronization and the CSAS of the coupled memristor-based circuits have potential applications in nonvolatile memories, neuromorphic devices to simulate learning, adaptive and spontaneous behaviors.

Secure communications via complex phase synchronization of pair complex chaotic structures with a similar structure of linear terms with modifying in nonlinear terms

In this paper, we discuss the idea of complex phase synchronization in complex nonlinear structures with chaotic conduct. The CPHS combines two types of common synchronizations, which are phase synchronization and anti phase synchronization. A general scheme has been proposed to study the CPHS. Through this scheme, complex control functions are assigned to obtain effective CPHS. For example, we study the CPHS in regards pair chaotic complex Lü structures including incompletely evolving for nonlinear terms. Numerical figures are drawn to prove our plan’s validity. The consequences of the CPHS are exploited in secure communications. The error function resulting from the definition of the CPHS was used as a key to retrieve the encrypted message.

In-Phase and Anti-Phase Synchronization in a Laser Frequency Comb.

Coupled clocks are a classic example of a synchronization system leading to periodic collective oscillations. Already in 1665, Christiaan Huygens described this phenomenon as a kind of "sympathy" among oscillators. In this work, we describe the formation of two types of laser frequency combs as a system of oscillators coupled through the beating of the lasing modes. We experimentally show two completely different types of synchronization in a quantum dot laser-in-phase and splay-phase states. Both states can be generated in the same device, just by varying the damping losses of the system. This modifies the coupling among the oscillators. The temporal laser output is characterized using both linear and quadratic autocorrelation techniques. Our results show that both pulses and frequency-modulated states can be generated on demand within the same device. These findings allow us to connect laser frequency combs produced by amplitude-modulated and frequency-modulated lasers and link these to pattern formation in coupled systems such as Josephson-junction arrays.

Fabrication of New Belousov-Zhabotinsky Micro-Oscillators on the Basis of Silica Gel Beads.

We have fabricated and examined silica gel beads loaded with a catalyst of the Belousov-Zhabotinsky (BZ) reaction, tris(2,2'-bipyridyl)ruthenium(II) chloride, Ru(bpy)3Cl2, the BZ beads. The abilities of silica gel and the widely used ion-exchange resin (Dowex 50WX2) BZ beads to oscillate in a catalyst-free BZ solution are compared. The period of the BZ oscillations increases with an increase in the diameter (40-250 μm) of both types of the BZ beads. The ability of the ion-exchange resin beads to hold catalyst molecules significantly decreases with a decrease in pH, while this value is less dependent on pH for the silica gel BZ beads. The diffusive coupling of two BZ beads separated by either aqueous or oil gaps is studied as well. For the aqueous gap less than 100 μm, the BZ beads of both types demonstrate in-phase synchronization. For the oil phase, the Dowex BZ beads are unable to oscillate for a long enough time and therefore cannot be synchronized, while the silica gel BZ beads are able to oscillate for several hours and demonstrate anti-phase synchronization for gaps less than 40 μm.

Three-dimensional wake transition in the flow over four square cylinders at low Reynolds numbers

The three-dimensional characteristics of the flow past four square cylinders in an in-line square configuration, with five spacing ratios ranging from 1.4 to 5, were studied in depth in this study. Direct numerical simulation of the spectral/hp element method was employed at Re = 150 and 200. The onset and evolution of various unstable modes were expounded in detail by means of three-dimensional vortices, energy curves, wake patterns, and force coefficients. At each spacing, the three-dimensional instability and the corresponding flow pattern were comprehensively analyzed to illustrate transitional features. Except for the existence of unstable mode A and mode B when spacing was considerably small and large, for most of the intermediate spacing ratios, the vortex structures were dominated by mode C instability, whose flow patterns all appeared as anti-phase synchronization. Through the evolution of flow patterns over time, the three-dimensional effects were already observed at a low Reynolds number of 150 because of the influence of the gap flow and the mutual interference of the wake. Under the transitional spacing for Re = 200, multiple modes were interfering fiercely with each other and appeared as chaotic states. Compared with other bluff body forms, the four square cylinders generated numerous discrepancies and new modal transitions in three-dimensional cases.

Secure Communication: Using Parallel Synchronization Technique On Novel Fractional Order Chaotic System

In this paper a novel 4-D fractional order chaotic system has been introduced. It has been synchronized in dislocated phase and anti-phase synchronization with its parallel systems by constructing non linear control inputs. The synchronization technique has been illustrated with help of an example in the field of secure communication.

Simulating oscillations of the system with piecewise-linear characteristics of elastic elements excited by self-synchronizing unbalance vibration exciters

Oscillations of a system of three solids with piecewise-linear characteristics of the elastic element between the bodies on which unbalanced vibration exciters of limited power are installed are considered in the paper. The modes of oscillations of the system near the second resonant frequency are analyzed. It is shown that intermittent interaction between system elements leads to a change in the dynamic characteristics of the system, including a change in the frequency range of stability of anti-phase synchronization of debalance rotation.

Experimental Investigation on Synchronization of Two Co-Rating Rotors Coupled With Nonlinear Springs

This work is a continuation and verification of the original literature by using experimental strategy. Based on the published paper, in order to avoid anti-phase synchronization with two co-rotating rotors system, a vibrating system with two co-rotating rotors installed with nonlinear springs have been proposed, and then, the synchronous condition and the synchronous criterion of the system are theoretically derived. From the analysis mentioned, it is shown that the synchronous state is mainly determined by the structural parameters of the coupling unit, coupling coefficients and positional parameters of the two exciters, etc. The main objective of the present work is to investigate the synchronous mechanism by experiments and simulations in this paper. Some simulation computations are firstly implemented to explain the synchronous mechanism of the system. Additionally, an experimental strategy with synchronous tests and dynamic characteristic tests of the vibrating system are carried out to validate the correctness of the simulation analysis. The simulations and experiments demonstrate that the nonlinear springs can overcome the difference of residual torques of the two motors to realize the synchronization of near zero phase difference under the condition of in-phase difference between two exciters. Finally, the error analysis results among the dynamic testing, synchronous testing results and simulations are discussed. This research can provide theoretical reference for designing large-sized and heavy-duty Vibrating Screens.

Weakly Nonlinear Theory for Oscillatory Dynamics in a One-Dimensional PDE-ODE Model of Membrane Dynamics Coupled by a Bulk Diffusion Field

We study the dynamics of systems consisting of two spatially segregated ODE compartments coupled through a one-dimensional bulk diffusion field. For this coupled PDE-ODE system, we first employ a multi-scale asymptotic expansion to derive amplitude equations near codimension-one Hopf bifurcation points for both in-phase and anti-phase synchronization modes. The resulting normal form equations pertain to any vector nonlinearity restricted to the ODE compartments. In our first example, we apply our weakly nonlinear theory to a coupled PDE-ODE system with Sel'kov membrane kinetics, and show that the symmetric steady state undergoes supercritical Hopf bifurcations as the coupling strength and the diffusivity vary. We then consider the PDE diffusive coupling of two Lorenz oscillators. It is shown that this coupling mechanism can have a stabilizing effect, characterized by a significant increase in the Rayleigh number required for a Hopf bifurcation. Within the chaotic regime, we can distinguish between synchronous chaos, where both the left and right oscillators are in-phase, and chaotic states characterized by the absence of synchrony. Finally, we compute the largest Lyapunov exponent associated with a linearization around the synchronous manifold that only considers odd perturbations. This allows us to predict the transition to synchronous chaos as the coupling strength and the diffusivity increase.

Synchronization and Bursting Activity in the Model for Two Predator-Prey Systems Coupled By Predator Migration

The papers is devoted to a model for two non-identical predator-prey communities coupled by migration and characterized by logistic growth of prey and Holling type II functional response. The coupling is a predator migration at constant weak rate. The non-identity is the difference in the prey growth rates or predator mortalities in each patch. We studied the equilibrium states of model and scenarios of loss of their stability and emerge of complex periodic solutions. It was shown that in some domains of the parameter space there is a bursting activity which are that the dynamics of two communities contain segments of slowly resting dynamic (as part of a fast-slow cycle or canard) and regular bursts of spikes. In the resting part, the dynamics of the second community, as a rule, follow the slow changes in the first community, i.e. the dynamics in different patches are synchronous. But in the fast part there is only phase synchronization between the fast-slow cycle in first patch and bursts in second. We classified the scenarios of transition between different types of bursting activity by location spiking manifold and canard. These types differ not so much in size, shape or numbers of spikes as in the order of bursts emerge relative a slow-fast cycle. In a typical case the start of burst (divergent fast oscillations) coincides with the minimum numbers or quasi-extinction of prey in the first patch. After a rapid increase in the prey number in the first patch, diverging fluctuations give way to damped in the second patch. Such dynamics correspond to the rhombus-wave shape of spikes cluster. Another case is interesting, when the burst of spikes is formed after the full recovery of prey and with a certain predator number in the first patch. In this case, the spikes cluster takes the shape of a triangle-wave or a truncated rhombus-wave. It was shown that transitions between these types of bursts are accompanied by a change in the oscillation period and the degree of synchronization. Triangular-wave bursters correspond to complete synchronization of the predator dynamics in the resting part and rhomboid-wave correspond to antiphase synchronization. In the fast part with many spikes, communities are completely asynchronous to each other.

On the Fluid Dynamical Effects of Synchronization in Side-by-Side Swimmers.

In-phase and anti-phase synchronization of neighboring swimmers is examined experimentally using two self-propelled independent flexible foils swimming side-by-side in a water tank. The foils are actuated by pitching oscillations at one extremity—the head of the swimmers—and the flow engendered by their undulations is analyzed using two-dimensional particle image velocimetry in their frontal symmetry plane. Following recent observations on the behavior of real fish, we focus on the comparison between in-phase and anti-phase actuation by fixing all other geometric and kinematic parameters. We show that swimming with a neighbor is beneficial for both synchronizations tested, as compared to swimming alone, with an advantage for the anti-phase synchronization. We show that the advantage of anti-phase synchronization in terms of swimming performance for the two-foil “school” results from the emergence of a periodic coherent jet between the two swimmers.

Antiphase chaotic synchronization enhancement in a vertical cavity surface emitting laser.

In this paper, we demonstrate experimentally that a vertical cavity surface emitting laser (VCSEL) exhibits an enhancement of nonlinear polarization dynamics, i.e., antiphase chaos synchronization and mode hopping, with optical feedback (OF). The rotating orthogonal polarization of a VCSEL is used as an external parameter to generate a chaotic signal when it is reflected back with a fixed bias current and strong OF signal. The intensity of the two linear polarization modes of the VCSEL is measured for a range of bias current, which provides detailed insights into its dynamic dependence. The results show that the antiphase chaotic synchronization is enhanced as the angle of orthogonal polarization of the OF is increased. Polarization modes are oscillated entirely in the chaotic regime in antiphase synchronization, with no time delay at the bias currents of 1.2 (low) and 1.7 mA (high). However, the synchronization quality of the two modes completely deteriorates when the bias current is increased to 1.7 mA at a polarization angle of 70°, where power mode differences are increased. This result shows that the power mode difference affects antiphase synchronization dynamics and thus destroys the mode-computation effects. In addition, polarization switching takes place at the polarization angles of 60° and about 33° at low and high bias currents, respectively. Polarization mode hopping is also observed, which is associated with improvement of the antiphase synchronization dynamics.