Antiphase Dynamics Research Articles

A Parrondo paradox in susceptible-infectious-susceptible dynamics over periodic temporal networks

Many social and biological networks periodically change over time with daily, weekly, and other cycles. Thus motivated, we formulate and analyze susceptible-infectious-susceptible (SIS) epidemic models over temporal networks with periodic schedules. More specifically, we assume that the temporal network consists of a cycle of alternately used static networks, each with a given duration. We observe a phenomenon in which two static networks are individually above the epidemic threshold but the alternating network composed of them renders the dynamics below the epidemic threshold, which we refer to as a Parrondo paradox for epidemics. We find that network structure plays an important role in shaping this phenomenon, and we study its dependence on the connectivity between and number of subpopulations in the network. We associate such paradoxical behavior with anti-phase oscillatory dynamics of the number of infectious individuals in different subpopulations.

Antiphase and in-phase dynamics in laser chain models with delayed bidirectional couplings

The radiation dynamics of a closed chain of lasers with optoelectronic delayed coupling is analyzed. We consider bidirectional couplings of two designs: (i) diffusion type with feedback and (ii) bidirectional type without feedback. Assuming that the number of lasers is sufficiently large, we propose integro-differential models for spatially distributed variables with periodic boundary conditions. The critical value of the coupling coefficient is determined at which the stationary state of laser generation spontaneously becomes unstable due to the presence of a delay in the coupling lines. Bifurcations of asymptotically infinite dimension are described. For both types of coupling, we obtain the same two-dimensional complex partial differential equation of the Ginzburg–Landau type (with the difference only in the coefficients) for the slowly varying amplitude of the fundamental harmonic. Using the simplest homogeneous solution of such a quasi-normal form, the oscillations of laser radiation in chains, which can be anti-phase or in-phase depending on the time delay and the design of the couplings, are analytically described.

Antarctic permafrost processes and antiphase dynamics of cold-based glaciers in the McMurdo Dry Valleys inferred from 10Be and 26Al cosmogenic nuclides

Abstract. Soil and sediment mixing and associated permafrost processes are not widely studied or understood in the McMurdo Dry Valleys of Antarctica. In this study, we investigate the stability and depositional history of near-surface permafrost sediments to ∼ 3 m depth in the Pearse and lower Wright valleys using measured cosmogenic 10Be and 26Al depth profiles. In Pearse Valley, we estimate a minimum depositional age of ∼ 74 ka for the active layer and paleoactive-layer sediments (< 0.65 m). Combined depth profile modelling of 10Be and 26Al gives a depositional age for near-surface (< 1.65 m) permafrost in Pearse Valley of 180 +20/-40 ka, implying that the deposition of permafrost sediments predates MIS 5 advances of Taylor Glacier. Deeper permafrost sediments (> 2.09 m) in Pearse Valley are thus inferred to have a depositional age of > 180 ka. At a coastal, lower-elevation site in neighbouring lower Wright Valley, 10Be and 26Al depth profiles from a second permafrost core exhibit near-constant concentrations with depth and indicate the sediments are either vertically mixed after deposition or sufficiently young so that post-depositional nuclide production is negligible relative to inheritance. 26Al/10Be concentration ratios for both depth profiles range between 4.0 and 5.2 and are all lower than the nominal surface production rate ratio of 6.75, indicating that prior to deposition, these sediments experienced complex, yet similar, exposure–burial histories. Assuming a single-cycle exposure–burial scenario, the observed 26Al/10Be ratios are equivalent to a total minimum exposure–burial history of ∼ 1.2 Myr. In proximity to the depth profile core site, we measured cosmogenic 10Be and 26Al in three granite cobbles from thin, patchy drift (Taylor 2 Drift) in Pearse Valley to constrain the timing of retreat of Taylor Glacier. Assuming simple continuous exposure, our minimum, zero-erosion exposure ages suggest Taylor Glacier partially retreated from Pearse Valley no later than 65–74 ka. The timing of retreat after 65 ka and until the Last Glacial Maximum (LGM) when Taylor Glacier was at a minimum position remains unresolved. The surface cobble ages and permafrost processes reveal Taylor Glacier advances during MIS 5 were non-erosive or mildly erosive, preserving the underlying permafrost sediments and peppering boulders and cobbles upon an older, relict surface. Our results are consistent with U/Th ages from central Taylor Valley and suggest changes in moisture delivery over Taylor Dome during MIS 5e, 5c, and 5a appear to be associated with the extent of the Ross Ice Shelf and sea ice in the Ross Sea. These data provide further evidence of antiphase behaviour through retreat of a peripheral lobe of Taylor Glacier in Pearse Valley, a region that was glaciated during MIS 5. We suggest a causal relationship of cold-based glacier advance and retreat that is controlled by an increase in moisture availability during retreat of sea ice and perhaps the Ross Ice Shelf, as well as, conversely, a decrease during times of sea ice and Ross Ice Shelf expansion in the Ross Sea.

Chaotic chimera attractors in a triangular network of identical oscillators.

A prominent type of collective dynamics in networks of coupled oscillators is the coexistence of coherently and incoherently oscillating domains known as chimera states. Chimera states exhibit various macroscopic dynamics with different motions of the Kuramoto order parameter. Stationary, periodic and quasiperiodic chimeras are known to occur in two-population networks of identical phase oscillators. In a three-population network of identical Kuramoto-Sakaguchi phase oscillators, stationary and periodic symmetric chimeras were previously studied on a reduced manifold in which two populations behaved identically [Phys. Rev. E 82, 016216 (2010)1539-375510.1103/PhysRevE.82.016216]. In this paper, we study the full phase space dynamics of such three-population networks. We demonstrate the existence of macroscopic chaotic chimera attractors that exhibit aperiodic antiphase dynamics of the order parameters. We observe these chaotic chimera states in both finite-sized systems and the thermodynamic limit outside the Ott-Antonsen manifold. The chaotic chimera states coexist with a stable chimera solution on the Ott-Antonsen manifold that displays periodic antiphase oscillation of the two incoherent populations and with a symmetric stationary chimera solution, resulting in tristability of chimera states. Of these three coexisting chimera states, only the symmetric stationary chimera solution exists in the symmetry-reduced manifold.

Feasibility of the Skin Electrodynamic Introscopy to Assess 2D Acid-Base Balance Dynamics

Synchronization is a universal phenomenon that occurs at all levels of the existence of living and inanimate matter. Shortly after enabling monitoring of the electrical impedance landscape of the skin, such phenomena were detected as dynamic clusters with in-phase and anti-phase dynamics. The behavior of these clusters turned out to be very sensitive to various endogenous and exogenous factors and was especially pronounced, for example, at the melanoma areas. Hypothesis of the acid-base balance fluctuations have been put forward as one of the most likely mechanisms for this phenomenon, since hydrogen ions are one of the main factors that determine tissue electrical conductivity. The purpose of this study was to obtain experimental evidence for this hypothesis. The 2D dynamics of glycolysis metabolism was studied on a yeast model as an adequate model of cancer cells. The image sequences reflected the dynamics of processes occurring at the intercellular and intracellular levels, in the form of current values of the 2D active and capacitive components of the impedance in the range of 2 kHz and 1 MHz. As a test factor, a single drop of glucose was used. The revealed effects of clusterization were found similar to those obtained earlier in human experiments. Specifically, these effects were also clearly manifested in the affected region. At the same time, the intercellular medium turned out to be the most rapidly responsive, while the intracellular response occurred with a significant delay but without so marked manifestations of anti-phase behavior. The observed effects are presumably a macroscopic manifestations of quorum sensing mechanisms and cooperative wave processes. We believe that the developed technology can be used as an inexpensive and non-invasive tool for both In vivo and In vitro real-time pH monitoring.

Correlated dynamics of three-body Rydberg superatoms

Owing to the long lifetime of Rydberg atom, easy to operate and easy to control the interaction between Rydberg atoms, Rydberg atom has attracted considerable attention in quantum information and quantum optics fields. Specially, the anti-blockade effect, as a physical resource, can be used to implement various tasks in quantum information processing. Based on the rigid dipole blockade, an ensemble of two-level Rydberg atoms trapped in three magneto-optical traps can be regarded as a superatom. Based on the superatom model, the in-phase and anti-phase dynamics of the three-body Rydberg superatoms are studied by adjusting the numbers of atoms, and the W state and two kinds of maximal entangled states are generated simultaneously. Our work has great potential applications in coherent manipulation and quantum information processing.The numerical simulations are performed based on the superatom model and thereby the formidable obstacle that the Hilbert space dimension grows exponentially with the particle number increasing can be completely removed. As a result, the quantum control and quantum entanglement can be achieved from the single-quanta level to the mesoscopic level.

Synchronization of interacted spiking neuronal networks with inhibitory coupling

• The synchronization index (SI) in two large interacted via inhibitory coupling networks oscillates periodically in time; the time intervals of high SI alternates with the time intervals of low SI. • The synchronization indexes in these networks exhibit either inphase or antiphase synchronization depending on the inhibitory coupling strength between them. We suppose that the underlying mechanism behind the antiphase dynamics lies in the cognitive resource redistribution between neuronal ensembles in the brain. • Excitatory coupling between the neurons inside the network affects the synchronization index. To maintain the neural network in the regimes of inphase or antiphase SI oscillations, we should keep a balance between excitatory and inhibitory connections. It suggests that the excitatory and the inhibitory currents should compensate each other. In other words, when one of them increases, the other must be increased too, and vice versa. • The coupling inside the input small network affects antiphase synchronization between two large networks. However, the scenario from positive and negative correlation and back between the large networks are only determined by inhibitory coupling between them. The development of mathematical models to describe neuronal interaction processes in the brain is a challenging task of nonlinear dynamics. Recent advances in biochemistry and neuroscience allow better understanding of biological mechanisms underlying the neuron functioning and synaptic connections between neurons. Moreover, significant progress in brain imaging sheds light on the structure of the brain network and certain aspects of neuronal dynamics. However, dynamical mechanisms leading to synchronization between different brain areas still remain unknown and require further investigation. To shed light on this issue, we consider two small-world networks of Hodgkin-Huxley neurons interacting via inhibitory coupling. We found that synchronization indices (SI) in both networks oscillate periodically in time, so that time intervals of high SI alternate with time intervals of low SI. Depending on the coupling strength, the two coupled networks can be in the regime of either in-phase or anti-phase synchronization. We suppose that the inherent mechanism behind such a behavior lies in the cognitive resource redistribution between neuronal ensembles of the brain.

Antiphase synchronization in multiplex networks with attractive and repulsive interactions.

A series of recent publications, within the framework of network science, have focused on the coexistence of mixed attractive and repulsive (excitatory and inhibitory) interactions among the units within the same system, motivated by the analogies with spin glasses as well as to neural networks, or ecological systems. However, most of these investigations have been restricted to single layer networks, requiring further analysis of the complex dynamics and particular equilibrium states that emerge in multilayer configurations. This article investigates the synchronization properties of dynamical systems connected through multiplex architectures in the presence of attractive intralayer and repulsive interlayer connections. This setting enables the emergence of antisynchronization, i.e., intralayer synchronization coexisting with antiphase dynamics between coupled systems of different layers. We demonstrate the existence of a transition from interlayer antisynchronization to antiphase synchrony in any connected bipartite multiplex architecture when the repulsive coupling is introduced through any spanning tree of a single layer. We identify, analytically, the required graph topologies for interlayer antisynchronization and its interplay with intralayer and antiphase synchronization. Next, we analytically derive the invariance of intralayer synchronization manifold and calculate the attractor size of each oscillator exhibiting interlayer antisynchronization together with intralayer synchronization. The necessary conditions for the existence of interlayer antisynchronization along with intralayer synchronization are given and numerically validated by considering Stuart-Landau oscillators. Finally, we also analytically derive the local stability condition of the interlayer antisynchronization state using the master stability function approach.

Stochastic transitions between in-phase and anti-phase synchronization in coupled map-based neural oscillators

A problem of mathematical modeling and analysis of complex oscillatory behavior in coupled nonlinear stochastic systems is considered. We study stochastic bifurcations and transitions between in-phase and anti-phase dynamics in two coupled map-based neural oscillators with regular and chaotic attractors. Interesting dynamical regimes of isolated and coupled oscillators are considered in a wide range of both deterministic and stochastic modes associated with in-phase and anti-phase synchronization. The comprehensive nonlinear and stochastic analyses using a stochastic sensitivity approach and confidence ellipses allowed us to reveal the geometry of multiple basins of attraction of coexisting states and confidence areas in both synchronous and asynchronous regimes. Coupling-induced and noise-induced transitions between order and chaos are also discussed.

In-phase and anti-phase entanglement dynamics of Rydberg atomic pairs.

We study the correlated evolutions of two far-spaced Rydberg atomic pairs with different resonant frequencies, interacting via van der Waals (vdW) potentials and driven by a common laser field. They are found to exhibit in-phase (anti-phase) beating dynamics characterized by identical (complementary) intra-pair entanglements under a specific condition in regard of inter-pair vdW potentials and driving field detunings. This occurs when each atomic pair just oscillates between its ground state and symmetric entangled state because its doubly excited state and asymmetric entangled state are forbidden due to rigid dipole blockade and perfect destructive interference, respectively. More importantly, optimal inter-pair overall entanglement can be attained at each beating node corresponding to semi-optimal intra-pair entanglements, and inevitable dissipation processes just result in a slow decay of intra-pair and inter-pair entanglements yet without destroying in-phase and anti-phase beating dynamics.

Optical rogue waves in coupled fiber Raman lasers.

For coupled linear cavity-random fiber Raman lasers, for the first time, to the best of our knowledge, we demonstrate a new mechanism of emergence of the random pulses, with the anomalous statistics satisfying optical rogue waves' criteria experimentally. The rogue waves appear as a result of the coupling of two Raman cascades, namely, a linear cavity laser with a wavelength of 1.55 µm and a random laser with a wavelength nearly 1.67 µm, along with coupling of the orthogonal states of polarization (SOPs). The coherent coupling of SOPs causes localization of the trajectories in the vicinity of these states, whereas polarization instability drives escape taking the form of chaotic oscillations. Antiphase dynamics in two cascades result in the suppression of low amplitude chaotic oscillations and enable the anomalous spikes, satisfying rogue waves criteria.

Fourier-Spectral Method for the Phase-Field Equations

In this paper, we review the Fourier-spectral method for some phase-field models: Allen–Cahn (AC), Cahn–Hilliard (CH), Swift–Hohenberg (SH), phase-field crystal (PFC), and molecular beam epitaxy (MBE) growth. These equations are very important parabolic partial differential equations and are applicable to many interesting scientific problems. The AC equation is a reaction-diffusion equation modeling anti-phase domain coarsening dynamics. The CH equation models phase segregation of binary mixtures. The SH equation is a popular model for generating patterns in spatially extended dissipative systems. A classical PFC model is originally derived to investigate the dynamics of atomic-scale crystal growth. An isotropic symmetry MBE growth model is originally devised as a method for directly growing high purity epitaxial thin film of molecular beams evaporating on a heated substrate. The Fourier-spectral method is highly accurate and simple to implement. We present a detailed description of the method and explain its connection to MATLAB usage so that the interested readers can use the Fourier-spectral method for their research needs without difficulties. Several standard computational tests are done to demonstrate the performance of the method. Furthermore, we provide the MATLAB codes implementation in the Appendix A.

Synchronization in coupled neural network with inhibitory coupling

A theoretical model of a network of neuron-like elements was constructed. The network included several subnetworks. The first subnetwork was used to translate a constant-amplitude signal into a spike sequence (conversion of amplitude to frequency). A similar process occurs in the brain when perceiving visual information. With an increase in the flow of information, the generation frequency of the neural ensemble participating in the processing increases. Further, the first subnetwork transmitted excitation to two large interconnected subnetworks. These subnetworks simulated the dynamics of the cortical neuronal populations. It was shown that in the presence of inhibitory coupling, the neuronal ensembles demonstrate antiphase dynamics. Various connectivity topologies and various types of neuron-like oscillators were investigated. We compare the results obtained in a discrete neuron model (Rulkov model) and a continuous-time model (Hodgkin-Huxley). It is shown that in the case of a discrete neuron model, the periodic dynamics is manifested in the alternate excitation of various neural ensembles. In the case of the continuous-time model, periodic modulation of the synchronization index of neural ensembles is observed.

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.

In-phase and antiphase dynamics of Rydberg atoms with distinguishable resonances

We study the correlated evolutions of two Rydberg atoms, interacting via a van der Waals (vdW) potential ${V}_{6}$ and driven by a laser field of detunings ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$. The two atoms may exhibit the in-phase dynamics with identical Rydberg populations or the antiphase dynamics with complementary Rydberg populations, depending on their initial states. For a moderate vdW potential far from the blockade regime, the in-phase or antiphase dynamics can be attained along two intersecting lines in the parameter space of ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$ with an exact or approximate figure of merit, respectively. Note, in particular, that the exact in-phase dynamics is trivial because it requires identical detunings while the approximate in-phase, exact antiphase, and approximate antiphase dynamics are nontrivial because they require distinct detunings. The specific requirements on ${\mathrm{\ensuremath{\Delta}}}_{1}$ and ${\mathrm{\ensuremath{\Delta}}}_{2}$ for both in-phase and antiphase dynamics can be understood by considering the balanced transitions from two initially populated states to two initially empty states in the double-atom state basis.

Investigation of the antiphase dynamics of the orthogonally polarized passively Q-switched Nd:YLF laser.

The antiphase dynamics of Q-switched orthogonally polarized emissions have been thoroughly investigated. A Nd:YLF crystal with the anisotropic thermal lensing effect is used as the gain medium for achieving dual polarized laser. By using the Cr4+:YAG saturable absorber, the passively Q-switched output shows intriguing switching dynamics, where the number of pulses for both polarized components within one switching period is directly determined by the power ratio between the orthogonally polarized emissions. Experimental results reveal that the pulse energies of every single pulse for both orthogonally polarized states are equal with the maximum value of 223 μJ. The pulse durations for π- and σ-polarization are measured to be 15 ns and 11 ns and the corresponding peak power levels are up to 15.0 kW and 20.3 kW, respectively.

Subharmonic anti-phase dynamics in coupled mode-locked semiconductor lasers.

We show that coupled mode-locked semiconductor lasers can operate in a subharmonic regime in which the two lasers pulsate in an anti-phase manner at one-half the fundamental mode-locking frequency of the solitary lasers. In the subharmonic mode, each pulse has almost twice the energy carried by the isolated lasers in the fundamental mode-locked regime and is also significantly shorter in duration. Depending on the unsaturated gain and coupling strength, the lasers can also exhibit bistability, perfect synchronization, and delayed synchronization, as well as three-halves and five-halves harmonic mode locking. The observed behaviors are robust and persist in the presence of noise.

Using Nonequilibrium Dynamics to Probe Competing Orders in a Mott-Peierls System.

Competition between ordered phases, and their associated phase transitions, are significant in the study of strongly correlated systems. Here, we examine one aspect, the nonequilibrium dynamics of a photoexcited Mott-Peierls system, using an effective Peierls-Hubbard model and exact diagonalization. Near a transition where spin and charge become strongly intertwined, we observe antiphase dynamics and a coupling-strength-dependent suppression or enhancement in the static structure factors. The renormalized bosonic excitations coupled to a particular photoexcited electron can be extracted, which provides an approach for characterizing the underlying bosonic modes. The results from this analysis for different electronic momenta show an uneven softening due to a stronger coupling near k_{F}. This behavior reflects the strong link between the fermionic momenta, the coupling vertices, and ultimately, the bosonic susceptibilities when multiple phases compete for the ground state of the system.

Observation of antiphase dynamics and harmonic resonance in a modulated dual-wavelength laser

We observe a nonlinear response of a dual-wavelength Nd:YAG laser when subjected to low-frequency periodic modulations of cavity losses. The modulation frequency is far from the relaxation oscillation frequency. The harmonic resonances of the two laser wavelengths associated with antiphase intensity oscillations are demonstrated and resonances up to the fourth order were observed. For relatively weak modulation, the intensity oscillation frequency of the laser is equal to the modulation frequency. Harmonic resonances occur under a stronger modulation. We find that more harmonic components appear when the modulation frequency is increased. Furthermore, with enhancing the modulation, the dominant frequency of the intensity oscillations of both wavelengths is shifted toward the higher-order harmonic frequency.

Chaos synchronization in vertical-cavity surface-emitting laser based on rotated polarization-preserved optical feedback.

In this paper, the influence of the rotating polarization-preserved optical feedback on the chaos synchronization of a vertical-cavity surface-emitting laser (VCSEL) is investigated experimentally. Two VCSELs' polarization modes (XP) and (YP) are gradually rotated and re-injected back into the VCSEL. The anti-phase dynamics synchronization of the two polarization modes is evaluated using the cross-correlation function. For a fixed optical feedback, a clear relationship is found between the cross-correlation coefficient and the polarization angle θp. It is shown that high-quality anti-phase polarization-resolved chaos synchronization is achieved at higher values of θp. The maximum value of the cross-correlation coefficient achieved is -0.99 with a zero time delay over a wide range of θp beyond 65° with a poor synchronization dynamic at θp less than 65°. Furthermore, it is observed that the antiphase irregular oscillation of the XP and YP modes changes with θp. VCSEL under the rotating polarization optical feedback can be a good candidate as a chaotic synchronization source for a secure communication system.