Repulsive Coupling Research Articles

Death transitions in attractive–repulsive coupled oscillators with higher-order interactions

The first-order phase transition from oscillation to steady state, known as explosive death (ED), is prevalent in various dynamical models. However, previous studies on ED have predominantly focused on interactions between pairs of elements. In this work, we investigate how death transitions occur when both pairwise and three-body interactions are present in an extended Van der Pol oscillator network with attractive–repulsive coupling. By examining both global and non-local interaction mechanisms, the impact of higher-order interactions on ED and the differences in the transition process are comprehensively analyzed. Firstly, we construct a diagram of the global dynamics in the context of higher-order and first-order coupling strengths, identifying that the higher-order interactions promote the onset of ED with a contribution comparable to that of first-order interactions. Specifically, for global coupling, the theoretical backward critical curves matching the numerical results are derived through linear stability analyses, showcasing a linear correlation with a slope of -1 between the higher-order and first-order coupling strengths. Under non-local coupling, fitting the numerically obtained backward critical curves likewise yields a consistent quantitative relationship. Additionally, during the transition process of ED, we discover intriguing coexisting states in the hysteresis area under non-local coupling, including the coexistence of chimera states with coherent or incoherent oscillation, and the coexistence of chimera states with oscillation death. This is attributed to symmetry breaking induced by non-local action. These findings enhance the understanding of higher-order interactions in complex systems and provide a fresh perspective for studying multi-stability behavior in biochemical and physical systems.

Realization of logic gates in bi-directionally coupled nonlinear oscillators.

Implementation of logic gates has been investigated in nonlinear dynamical systems from various perspectives over the years. Specifically, logic gates have been implemented in both single nonlinear systems and coupled nonlinear oscillators. The majority of the works in the literature have been done on the evolution of single oscillators into OR/AND or NOR/NAND logic gates. In the present study, we demonstrate the design of logic gates in bi-directionally coupled double-well Duffing oscillators by applying two logic inputs to the drive system alone along with a fixed bias. The nonlinear system, comprising both bi-directional components, exhibits varied logic behaviors within an optimal range of coupling strength. Both attractive and repulsive couplings yield similar and complementary logic behaviors in the first and second oscillators. These couplings play a major role in exhibiting fundamental and universal logic gates in simple nonlinear systems. Under a positive bias, both the first and second oscillators demonstrate OR logic gate for the attractive coupling, while exhibiting OR and NOR logic gates, respectively, for the repulsive coupling. Conversely, under a negative bias, both the first and second oscillators display AND logic gate for the attractive coupling, and AND and NAND logical outputs for the repulsive coupling. Furthermore, we confirm the robustness of the bi-directional oscillators against moderate noise in maintaining the desired logical outputs.

Nonlinear vibration energy harvesting via parametric excitation: Snap-through with time-varying potential wells

This study introduces a novel method to improve snap-through transitions in a parametrically excited cantilever-based energy harvester featuring repulsive magnetic coupling. The aim is to enhance the efficiency of a piezoelectric energy harvester while broadening its operational frequency range. The design incorporates an oscillating substructure that magnetically interacts with the beam, promoting easier transitions. Additionally, this setup capitalizes on the resonant energy of the substructure to optimize energy capture. This study addresses a previously unexplored limitation in the directly excited counterpart by optimizing the use of substructure’s resonant energy to significantly improve the energy harvesting device’s efficiency. We present a theoretical model based on the Hamilton principle, which is solved numerically. Comprehensive experimental studies are conducted to validate the theoretical results, showing a strong correlation between the experimental outcomes and theoretical predictions. The findings indicate that an oscillating substructure with a tailored natural frequency close to twice that of the parametrically excited piezoelectric beam can induce time-varying potential wells to facilitate snap-through transitions. Despite the damping coefficient of the piezoelectric beam being three times higher than that of its simple beam counterpart, periodic perturbations still effectively expand its instability region. This enlarged instability region, resulting from such perturbations, not only exhibits broadband characteristics but also facilitates efficient energy harvesting at lower excitation levels.

Consistent Second-Order Treatment of Spin-Orbit Coupling and Dynamic Correlation in Quasidegenerate N-Electron Valence Perturbation Theory.

We present a formulation and implementation of second-order quasidegenerate N-electron valence perturbation theory (QDNEVPT2) that provides a balanced and accurate description of spin-orbit coupling and dynamic correlation effects in multiconfigurational electronic states. In our approach, the energies and wave functions of electronic states are computed by treating electron repulsion and spin-orbit coupling operators as equal perturbations to the nonrelativistic complete active-space wave functions, and their contributions are incorporated fully up to the second order. The spin-orbit effects are described using the Breit-Pauli (BP) or exact two-component Douglas-Kroll-Hess (DKH) Hamiltonians within spin-orbit mean-field approximation. The resulting second-order methods (BP2- and DKH2-QDNEVPT2) are capable of treating spin-orbit coupling effects in nearly degenerate electronic states by diagonalizing an effective Hamiltonian expanded in a compact non-relativistic basis. For a variety of atoms and small molecules across the entire periodic table, we demonstrate that DKH2-QDNEVPT2 is competitive in accuracy with variational two-component relativistic theories. BP2-QDNEVPT2 shows high accuracy for the second- and third-period elements, but its performance deteriorates for heavier atoms and molecules. We also consider the first-order spin-orbit QDNEVPT2 approximations (BP1- and DKH1-QDNEVPT2), among which DKH1-QDNEVPT2 is reliable but less accurate than DKH2-QDNEVPT2. Both DKH1- and DKH2-QDNEVPT2 hold promise as efficient and accurate electronic structure methods for treating electron correlation and spin-orbit coupling in a variety of applications.

Chimera states in fractional-order coupled Rayleigh oscillators

Chimera states, characterized by the coexistence of synchronized and desynchronized oscillators, have been extensively described via integer differential equations over the past few decades. However, it is still unclear whether and under which conditions chimera states will appear in terms of the coupled systems involving fractional derivatives. In this work, we investigate the chimera states of Rayleigh oscillators in the fractional-order systems with attractive and repulsive couplings. Firstly, we introduce the repulsive control factor and show the various transition routes from the desynchronized state to the incoherent oscillation death by altering this factor and the fractional-order derivatives. Then, it is demonstrated that as the coupling strength varies, a vast repertoire of interesting collective behaviors will emerge, such as synchronization, solitary state, traveling wave, traveling chimera, oscillatory cluster, imperfect traveling chimera state, imperfect amplitude chimera state, and chimera death. Finally, we discuss the effect of attractive and repulsive couplings and find that decreasing the repulsive control factor can reduce the repulsive interaction, allowing the attractive coupling to dominate and promote the emergence of the coherent state.

Explosive and semi-explosive transitions in parametrically perturbed systems

The phenomenon of transition between steady states, namely amplitude death and oscillation death, is identified in certain models of coupled parametrically driven nonlinear oscillators. Intriguingly, the nature of the transition is explosive. It is significant to note that this observation of explosive transition has been made in systems of identical coupled oscillators with repulsive mean-field coupling. In particular, we find that when the coupling strength increases, there are semi-explosive transitions in parametrically perturbed duffing oscillators and explosive transitions in parametrically perturbed van der Pol oscillators. We obtain analytical expressions for the critical bifurcation points through linear stability analysis. Detailed numerical studies have been performed to confirm the phenomenon.

Validity of annealed approximation in a high-dimensional system

This study investigates the suitability of the annealed approximation in high-dimensional systems characterized by dense networks with quenched link disorder, employing models of coupled oscillators. We demonstrate that dynamic equations governing dense-network systems converge to those of the complete-graph version in the thermodynamic limit, where link disorder fluctuations vanish entirely. Consequently, the annealed-network systems, where fluctuations are attenuated, also exhibit the same dynamic behavior in the thermodynamic limit. However, a significant discrepancy arises in the incoherent (disordered) phase wherein the finite-size behavior becomes critical in determining the steady-state pattern. To explicitly elucidate this discrepancy, we focus on identical oscillators subject to competitive attractive and repulsive couplings. In the incoherent phase of dense networks, we observe the manifestation of random irregular states. In contrast, the annealed approximation yields a symmetric (regular) incoherent state where two oppositely coherent clusters of oscillators coexist, accompanied by the vanishing order parameter. Our findings imply that the annealed approximation should be employed with caution even in dense-network systems, particularly in the disordered phase.

Hamilton energy variations in memristive Hindmarsh–Rose neurons under attractive and repulsive couplings

Hamilton energy variations in memristive Hindmarsh–Rose neurons under attractive and repulsive couplings

Insulator-to-metal transition, magnetic anisotropy, and improved TC in a ferrimagnetic La2CoIrO6: strain influence.

The elegant interactions between Coulomb repulsion and spin-orbit coupling in Ir-based double perovskite oxides (DPO) normally induce peculiar magnetic behavior. Herein, we investigate the effect of the development of biaxial [110] strain on the formation energetics, and electronic and magnetic properties of the La2CoIrO6 DPO employing density functional theory calculations. Our results reveal that the unstrained motif is a Mott-insulator achieving an energy band gap of 0.35 eV with a ferrimagnetic (FiM) ground state, which essentially arises due to anti-ferromagnetic (AFM) coupling between the half-occupied Co t2g and partially occupied Ir t2g/empty eg orbitals via oxygen 2p states. Along with this, it is found that [001] (c-axis) is the easy magnetic axis, which results in 12.5 meV total energy per u.c., obtaining a large anisotropy constant of 0.8 × 108 erg cm-3. The computed partial spin-magnetic moments on the Co/Ir ion are 2.64/-0.46 μB, where the negative sign on the Ir ion moment confirms the AFM interactions between them. Additionally, the t2g/eg and t2g orbital characteristics of Co2+ and Ir4+ ions are visible in the spin-magnetization density isosurfaces plot, respectively. Likewise, the estimated Curie temperature (TC) using the Heisenberg model is 104 K, which is in agreement with the experimentally observed value of 94/97 K. Interestingly, an insulator-to-metal transition is achieved at a critical compressive strain of -6% with a robust FiM state, where the Co 3dxy and Ir 5dx2-y2 orbitals are mainly responsible for metallicity. Simultaneously, the magnetocrystalline anisotropy energy and TC can be sufficiently enhanced by applying compressive strain due to enhancement in the structural distortions. So this work suggested that the strain strategy is an efficient approach to tuning the properties of the compounds for their feasible realization in spintronics.

Cyclops states in repulsive theta-neuron networks

Networks of phase oscillators have become a widely established paradigmatic model for studying emergent collective behavior across several real-world systems, including neuronal networks, populations of chemical oscillators, and power grids. The Kuramoto model, involving one-dimensional or two-dimensional phase oscillators, demonstrates the potential for networks to showcase exceptional collective dynamics. This encompasses various outcomes such as full, partial, explosive, and asymmetry-induced synchronization, clusters, chimeras, solitary states, and generalized splay states. Notably, increasing all-to-all coupling in the classical Kuramoto model induces full synchronization as the most probable outcome and dominant rhythm. Kuramoto networks with repulsive coupling usually display splay, generalized, and cluster splay states, but the conditions under which a certain rhythm can arise and prevail are not entirely understood. Equally important for connecting Kuramoto networks to practical physical systems is understanding the function of higher-order coupling terms. These terms display a Fourier decomposition of a general 2π-periodic interaction function [1]. Previous studies have demonstrated that the inclusion of higher-order terms in the classical Kuramoto model of oscillators with all-to-all attractive coupling can lead to multiple synchronous states and switching between synchronization clusters. However, the impact of higher-order coupling modes on rhythm generation in repulsive networks remains unexplored. In this work, we present significant progress in addressing the critical issue related to repulsive Kuramoto–Sakaguchi networks of phase oscillators with phase-lagged first-order and higher-order coupling. We demonstrate that weakly repulsive networks of even and odd numbers of oscillators with first-order coupling are dominated by two-cluster and three-cluster splay states, respectively. The three-cluster splay states consist of two distinct coherent clusters and one solitary oscillator. These tripod states can be considered a fusion of a two-body chimera and a solitary state. We have dubbed these patterns of three oscillators as “Cyclops states” in reference to the Greek mythological giant with a single eye. The solitary oscillator and synchronous clusters respectively represent the Cyclops’ eye and shoulders. We present a remarkable discovery that the inclusion of higher-order coupling modes leads to worldwide stability of cyclops states across almost the entire range of the phase-lag parameter controlling repulsion [2]. Beyond the Kuramoto oscillators, we demonstrate the robust presence of this effect in networks of canonical theta-neurons with adaptive coupling. Furthermore, our results provide insight into identifying dominant rhythms within repulsive physical and biological networks.

Phase transitions on a multiplex of swarmalators.

Dynamics of bidirectionally coupled swarmalators subject to attractive and repulsive couplings is analyzed. The probability of two elements in different layers being connected strongly depends on a defined vision range r_{c} which appears to lead both layers in different patterns while varying its values. Particularly, the interlayer static sync π has been found and its stability is proven. First-order transitions are observed when the repulsive coupling strength σ_{r} is very small for a fixed r_{c} and, moreover, in the absence of the repulsive coupling, they also appear for sufficiently large values of r_{c}. For σ_{r}=0 and for sufficiently small values of r_{c}, both layers achieve a second-order transition in a surprising two steps that are characterized by the drop of the energy of the internal phases while increasing the value of the interlayer attractive coupling σ_{a} and later a smooth jump, up to high energy value where synchronization is achieved. During these transitions, the internal phases present rotating waves with counterclockwise and later clockwise directions until synchronization, as σ_{a} increases. These results are supported by simulations and animations added as supplemental materials.

Bidirectional Negative Coupling Induced Dynamical Patterns in a Branched Epoxy-Based Dual-Electrode Microchip Flow Cell

In this contribution, we investigated the spatiotemporal pattern formation of oscillatory electrodissolution of nickel in sulfuric acid with two micro-wires placed in two branches of a microfluidic flow cell. In the flow channel, the reference and counter electrodes are placed at the opposite end of the branched flow channel (contralateral placement). A theory based on modeling the potential drop in the flow channel and the interactions between the reactions showed the presence of bidirectional negative electrical coupling between the electrode potential variables. Experiments and numerical simulations with a kinetic model showed that such bidirectional negative coupling could induce complex dynamics. The experiments showed that anti-phase synchronization occurred only when electrodes were placed in the middle of the branched flow channel. When the electrodes were close to beginning or the end of the channels, where the reference and counter electrodes were placed, respectively, no phase locking was observed. The coupling is intensified in magnitude when the electrodes are in the middle of the flow channel, which maximizes the loop current which can flow towards the reference electrode. The nature of the bidirectional coupling is confirmed in independent experiments with synchrony analysis using the Hilbert transform. Additionally, to further verify the nature of the migration current coupling, a data driven approach, inferring connections of networks (ICON), was utilized. Analysis using the ICON technique showed that the synchronization patterns can be described by a phase repulsive bidirectional coupling. The findings indicate that contralateral placement should be used with great care in electroanalytical application with reactions that exhibit negative differential resistance(NDR) region, e.g., due to passivation or adsorption of an inhibitor. Ultimately, revealing connectivity is essential to characterize the dynamical structures and functions of networks, which in turn, leads to the fundamental understanding of many real-world complex systems such as the topology of the physical or functional connections of neurons in the brain.

Critical behaviour near critical end points and tricritical points in disordered spin-1 ferromagnets

Critical end points and tricritical points are multicritical points that separate lines of continuous transitions from lines of first order transitions in the phase diagram of many systems. In models like the spin-1 disordered Blume–Capel model and the repulsive Blume–Emery–Griffiths model, the tricritical point splits into a critical end point and a bicritical end point with an increase in disorder and repulsive coupling strength respectively. In order to make a distinction between these two multicritical points, we investigate and contrast the behaviour of the first order phase boundary and the co-existence diameter around them.

Equation of state for strange quark matter: Linking the Nambu–Jona-Lasinio model to perturbative QCD

Neutron star constraints and {\it ab initio} pQCD evaluations require the EoS representing cold quark matter to be stiff at intermediate baryonic densities and soft at high-$n_B$. Here, I suggest that the three flavor NJL model with a density dependent repulsive coupling, $G_V(\mu)$, can generate an EoS which interpolates between these two regimes. Such an interpolation requires repulsion to start decreasing with the chemical potential just after chiral transition takes place. The conjecture behind this mechanism is that repulsion should be necessary only as long as the quark condensates, which dress the effective masses, have non-vanishing values. This assumption guarantees that an initially hard EoS suffers a conspicuous change of slope at ${\cal E} \simeq 0.7 \,{\rm GeV fm^{-3}}$ converging to the pQCD results at higher energy densities. Then, the speed of sound naturally reaches a non-conformal maximum at $n_B = 3.23 \, n_0 = 0.52 \, {\rm fm}^{-3}$ while the trace anomaly remains positive for all densities, in agreement with recent investigations. These non-trivial results {\it cannot} be simultaneously obtained when $G_V$ vanishes or has a fixed value. Therefore, the simple model proposed here is able to link the (non-perturbative) region of intermediate densities to the region where pQCD becomes reliable.

Interlayer antisynchronization in degree-biased duplex networks.

With synchronization being one of nature's most ubiquitous collective behaviors, the field of network synchronization has experienced tremendous growth, leading to significant theoretical developments. However, most previous studies consider uniform connection weights and undirected networks with positive coupling. In the present article, we incorporate the asymmetry in a two-layer multiplex network by assigning the ratio of the adjacent nodes' degrees as the weights to the intralayer edges. Despite the presence of degree-biased weighting mechanism and attractive-repulsive coupling strengths, we are able to find the necessary conditions for intralayer synchronization and interlayer antisynchronization and test whether these two macroscopic states can withstand demultiplexing in a network. During the occurrence of these two states, we analytically calculate the oscillator's amplitude. In addition to deriving the local stability conditions for interlayer antisynchronization via the master stability function approach, we also construct a suitable Lyapunov function to determine a sufficient condition for global stability. We provide numerical evidence to show the necessity of negative interlayer coupling strength for the occurrence of antisynchronization, and such repulsive interlayer coupling coefficients cannot destroy intralayer synchronization.

Explosive synchronization in phase oscillator populations with attractive and repulsive adaptive interactions

The attractive and repulsive adaptive coupling schemes among dynamical agents are ubiquitous in systems ranging from physics, biology to neuroscience, which have attracted increasing interest and ample attention during recent years. Here, we extend the classical Kuramoto model to the coupling with mixed signs by considering a particular adaptive scheme in a system of globally coupled phase oscillators. The time-varying coupling weight between each pair of oscillators is correlated with the local coherence that involves according to a nonlinear differential equation. The studied model is capable of capturing the essential properties of the explosive synchronization induced by the adaptive interactions. We carry out extensive simulations to explore the collective dynamics in different perspectives. Remarkably, we reveal that the occurrence of the abrupt transitions of the macroscopic overall weights, as well as the emergence of the correlations between the microscopic structure features (including degrees and frequency dissasortativity) and local dynamics trigger the explosive synchronization, which manifests the suppression rule for the formation of small synchronized clusters. Furthermore, we provide an analytical treatment for the reduced system that allows us to grasp the underlying mechanism of the observed phenomena. Our study can deepen the understanding of the explosive synchronization transitions and other related abrupt dynamic phenomena occurring in networked oscillators with generic adaptive schemes.

Cyclops States in Repulsive Kuramoto Networks: The Role of Higher-Order Coupling.

Repulsive oscillator networks can exhibit multiple cooperative rhythms, including chimera and cluster splay states. Yet, understanding which rhythm prevails remains challenging. Here, we address this fundamental question in the context of Kuramoto-Sakaguchi networks of rotators with higher-order Fourier modes in the coupling. Through analysis and numerics, we show that three-cluster splay states with two distinct coherent clusters and a solitary oscillator are the prevalent rhythms in networks with an odd number of units. We denote such tripod patterns cyclops states with the solitary oscillator reminiscent of the Cyclops' eye. As their mythological counterparts, the cyclops states are giants that dominate the system's phase space in weakly repulsive networks with first-order coupling. Astonishingly, the addition of the second or third harmonics to the Kuramoto coupling function makes the cyclops states global attractors practically across the full range of coupling's repulsion. Beyond the Kuramoto oscillators, we show that this effect is robustly present in networks of canonical theta neurons with adaptive coupling. At a more general level, our results suggest clues for finding dominant rhythms in repulsive physical and biological networks.

Negative refraction in hyperbolic hetero-bicrystals.

We visualized negative refraction of phonon polaritons, which occurs at the interface between two natural crystals. The polaritons-hybrids of infrared photons and lattice vibrations-form collimated rays that display negative refraction when passing through a planar interface between the two hyperbolic van der Waals materials: molybdenum oxide (MoO3) and isotopically pure hexagonal boron nitride (h11BN). At a special frequency ω0, these rays can circulate along closed diamond-shaped trajectories. We have shown that polariton eigenmodes display regions of both positive and negative dispersion interrupted by multiple gaps that result from polaritonic-level repulsion and strong coupling.

Pair Density Wave Order from Electron Repulsion.

A pair density wave (PDW) is a superconductor whose order parameter is a periodic function of space, without an accompanying spatially uniform component. Since PDWs are not the outcome of a weak-coupling instability of a Fermi liquid, a generic pairing mechanism for PDW order has remained elusive. We describe and solve models having robust PDW phases. To access the intermediate coupling limit, we invoke large-N limits of Fermi liquids with repulsive BCS interactions that admit saddle point solutions. We show that the requirements for long-range PDW order are that the repulsive BCS couplings must be nonmonotonic in space and that their strength must exceed a threshold value. We obtain a phase diagram with both finite temperature transitions to PDW order and a T=0 quantum critical point, where non-Fermi liquid behavior occurs.

Synchronization in repulsively coupled oscillators.

A long-standing expectation is that two repulsively coupled oscillators tend to oscillate in opposite directions. It has been difficult to achieve complete synchrony in coupled identical oscillators with purely repulsive coupling. Here, we introduce a general coupling condition based on the linear matrix of dynamical systems for the emergence of the complete synchronization in pure repulsively coupled oscillators. The proposed coupling profiles (coupling matrices) define a bidirectional cross-coupling link that plays the role of indicator for the onset of complete synchrony between identical oscillators. We illustrate the proposed coupling scheme on several paradigmatic two-coupled chaotic oscillators and validate its effectiveness through the linear stability analysis of the synchronous solution based on the master stability function approach. We further demonstrate that the proposed general condition for the selection of coupling profiles to achieve synchronization even works perfectly for a large ensemble of oscillators.