Increasing Coupling Strength Research Articles

Dynamics of coexisting rotating waves in unidirectional rings of bistable Duffing oscillators

We study the dynamics of multistable coexisting rotating waves that propagate along a unidirectional ring consisting of coupled double-well Duffing oscillators with different numbers of oscillators. By employing time series analysis, phase portraits, bifurcation diagrams, and basins of attraction, we provide evidence of multistability on the route from coexisting stable equilibria to hyperchaos via a sequence of bifurcations, including the Hopf bifurcation, torus bifurcations, and crisis bifurcations, as the coupling strength is increased. The specific bifurcation route depends on whether the ring comprises an even or odd number of oscillators. In the case of an even number of oscillators, we observe the existence of up to 32 coexisting stable fixed points at relatively weak coupling strengths, while a ring with an odd number of oscillators exhibits 20 coexisting stable equilibria. As the coupling strength increases, a hidden amplitude death attractor is born in an inverse supercritical pitchfork bifurcation in the ring with an even number of oscillators, coexisting with various homoclinic and heteroclinic orbits. Additionally, for stronger coupling, amplitude death coexists with chaos. Notably, the rotating wave speed of all coexisting limit cycles remains approximately constant and undergoes an exponential decrease as the coupling strength is increased. At the same time, the wave frequency varies among different coexisting orbits, exhibiting an almost linear growth with the coupling strength. It is worth mentioning that orbits originating from stronger coupling strengths possess higher frequencies.

Robustness of interdependent higher-order networks

In real complex systems, interactions occur not only between a pair of nodes, but also in groups of three or more nodes, which can be abstracted as higher-order structures in the networks. The simplicial complex is one of a model to represent systems with both low-order and higher-order structures. In this paper, we study the robustness of interdependent simplicial complexes under random attacks, where the complementary effects of the higher-order structure are introduced. When a higher-order node in a 2-simplex fails, its dependent node in the other layer survives with a certain probability due to the complementary effects from the 2-simplex. By using the percolation method, we derive the percolation threshold and the size of the giant component when the cascading failure reaches its steady state. The simulation results agree well with analytical predictions. We find that the type of phase transition changes from the first-order to the second-order when the complementary effect of the higher-order structure on the dependent node increases or the number of 2-simplices in the interdependent simplicial complex increases. While the interlayer coupling strength increases, the type of phase transition changes from the second-order to the first-order. In particular, even if the higher-order interactions do not provide complementary effects for dependent nodes, the robustness of the interdependent heterogeneous simplicial complex is higher than that of the ordinary interdependent network with the same average degree due to the existence of 2-simplices in the system. This study furthers our understanding in the robustness of interdependent higher-order networks.

Reduced Plasticity in Coupling Strength in the Aging SCN Clock as Revealed by Kuramoto Modeling.

The mammalian circadian clock is located in the suprachiasmatic nucleus (SCN) and consists of a network of coupled neurons, which are entrained to the environmental light-dark cycle. The phase coherence of the neurons is plastic and driven by the duration of daylight. With aging, the capacity to behaviorally adapt to seasonal changes in photoperiod reduces. The mechanisms underlying photoperiodic adaptation are largely unknown, but are important to unravel for the development of novel interventions to improve the quality of life of the elderly. We analyzed the phase coherence of single-cell PERIOD2::LUCIFERASE (PER2::LUC) expression rhythms in the SCN of young and old mice entrained to either long or short photoperiod. The phase coherence was used as input to a 2-community noisy Kuramoto model to estimate the coupling strength between and within neuronal subpopulations. The model revealed a correlation between coupling strength and photoperiod-induced changes in the phase relationship among neurons, suggesting a functional link. We found that the SCN of young mice adapts in coupling strength over a large range, with weak coupling in long photoperiod (LP) and strong coupling in short photoperiod (SP). In aged mice, we also found weak coupling in LP, but a reduced capacity to reach strong coupling in SP. The inability to respond with an increase in coupling strength suggests that manipulation of photoperiod is not a suitable strategy to enhance clock function with aging. We conclude that the inability of aged mice to reach strong coupling contributes to deficits in behavioral adaptation to seasonal changes in photoperiod.

Propagation Effect of Epileptic Seizures in a Coupled Thalamocortical Network

Epileptic seizures have spatial features related to the propagation of seizure waves. As the main characteristic of absence seizures, 2–4[Formula: see text]Hz spike-wave discharges (SWDs) originate from the cortices and are maintained by the thalamus. In this study, we explore the onset and propagation effect of absence seizures based on a thalamocortical model. First, we develop a two-compartment model and consider the autapse of the thalamic reticular nucleus as a crucial parameter to investigate transition behaviors. Moreover, we present dynamical mechanisms through bifurcation analysis. Simulation results show that the absence seizures can be induced and advanced as the coupling strength increases. Second, we investigate excitatory and inhibitory coupling functions in a three-compartment model. Our research indicates that the excitatory coupling function can lead to SWDs when all the compartments are initially saturated. In the process of propagation, excitatory coupling also gives rise to SWDs in normal compartments, whereas inhibitory coupling plays a limited role. Finally, we reproduce the above results in a 10-compartment model and verify the robustness against the variation of the number of modules. This work may shed new light on the field of seizure propagation and provide potential dynamical mechanisms.

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.

Chaos in coupled heteroclinic cycles and its piecewise-constant representation

We consider two robust heteroclinic cycles rotating in opposite directions, coupled by diffusive terms. A complete synchronization is impossible in this system. Numerical studies show that chaos is abundant at low levels of coupling. With increasing coupling strength, several symmetry-changing transitions are observed, and finally, a stable periodic regime appears via an inverse period-doubling cascade. To reveal the behavior at extremely small couplings, a piecewise constant model for the dynamics is proposed. Within this model, we numerically construct a Poincaré map for a chaotic state, which appears to be an expanding non-invertible circle map, thus confirming the abundance of chaos in the small coupling limit. We also show that within the piecewise constant description, there is a set of periodic solutions with different phase shifts between subsystems due to dead zones in the coupling.

Chimera states in multiplex networks: Chameleon-like across-layer synchronization.

Different across-layer synchronization types of chimera states in multilayer networks have been discovered recently. We investigate possible relations between them, for example, if the onset of some synchronization type implies the onset of some other type. For this purpose, we use a two-layer network with multiplex inter-layer coupling. Each layer consists of a ring of non-locally coupled phase oscillators. While oscillators in each layer are identical, the layers are made non-identical by introducing mismatches in the oscillators' mean frequencies and phase lag parameters of the intra-layer coupling. We use different metrics to quantify the degree of various across-layer synchronization types. These include phase-locking between individual interacting oscillators, amplitude and phase synchronization between the order parameters of each layer, generalized synchronization between the driver and response layer, and the alignment of the incoherent oscillator groups' position on the two rings. For positive phase lag parameter mismatches, we get a cascaded onset of synchronization upon a gradual increase of the inter-layer coupling strength. For example, the two order parameters show phase synchronization before any of the interacting oscillator pairs does. For negative mismatches, most synchronization types have their onset in a narrow range of the coupling strength. Weaker couplings can destabilize chimera states in the response layer toward an almost fully coherent or fully incoherent motion. Finally, in the absence of a phase lag mismatch, sufficient coupling turns the response dynamics into a replica of the driver dynamics with the phases of all oscillators shifted by a constant lag.

First-order quantum phase transition in the squeezed Rabi model

Quantum phase transition and entanglement in the Rabi model with a squeezed light are investigated. We find a special unitary-transformation method that removes the nonintegrable squeezing and counterrotating-wave interactions when the qubit frequency is close to the field frequency. The analytical ground state agrees well with the numerical solution. We demonstrate that the ground state exhibits a first-order quantum phase transition at a critical point induced linearly by the squeezed light. This quantum phase transition requires neither multiple qubits nor an infinite ratio of qubit frequency to field frequency, which solves a critical problem for the theory and experiment in Rabi model. As the qubit-field coupling strength increases, the ground-state entanglement reaches its maximum value at the critical point.

Chimera states in coupled pendulum with higher-order interaction

The study of chimera states in non-pairwise interaction networks is one of the challenging issues in current research. In recent work [S. Kundu and D. Ghosh (2022)], it was discovered that higher-order interactions promote chimera states in nonlocally coupled identical Kuramoto oscillators. In this work, we investigate a higher-order interaction network of a nonlocally coupled pendulum with inertia. By studying pairwise and non-pairwise interaction strengths, we observe different collective states, like synchronization, coherent traveling waves, single-head, multi-head, imperfect traveling chimera states, and incoherent states. In particular, we discover a novel non-stationary chimera state, namely a penetrable traveling chimera state, where the oscillators in the coherent domain of the network travel regularly while others drift randomly in the incoherent domain. We make a map of all the spatiotemporal behaviors in the parameter space of interactive coupling and identify the transition from non-stationary chimeras to coherent states passing through stationary chimeras. As higher-order coupling strength increases, collective dynamics eventually transit to coherence since higher-order interactions are conducive to the emergence of a multi-stable state even without non-pairwise interactions, as demonstrated by the basin stability simulations. After analyzing the damping effects, we consolidate the generality of damping in eradicating dynamical behavior. The abundant dynamics appear, then deteriorate, and even disappear in the corresponding model with inertia. The study of rich dynamic behavior is essential for facilitating an understanding of the impact of higher-order interactions and damping effects on the dynamics of complex real-world networks.

Unified treatment for scattering, absorption, and photoluminescence of coupled metallic nanoparticles with vertical polarized excitation

Optical properties of coupled metallic nanoparticles (MNPs) have been widely reported due to their unique characteristics such as peak shift/splitting of the coupling spectra and electromagnetic enhancement at subwavelength scale, etc. In a previous work, we have investigated the coupling spectra of two coupled MNPs with parallel polarized excitation. In this study, we investigate the vertical polarization case in detail. Different from the parallel one, the vertical one has its unique properties: (a) three coupling coefficients; (b) positive coupling terms in the coupling equations; (c) blue-shifts of the peaks with the increasing coupling strength for identical MNPs spectra, including scattering, absorption, and photoluminescence (PL). The model shows that for the two resonant MNPs, the spectra reveal only one mode that blue shifts as the coupling strength increases; while for the two non-resonant MNPs, the spectra reveal two splitting modes, one of which blue shifts and the other of which red shifts as the coupling strength increases. The relative intensity of the two modes varies with the coupling strength. Furthermore, the PL efficiency (relative to the scattering) is about the order of 10−2. Comparison with published experimental results shows the validity of this model. This work provides a deeper understanding on the optical properties of coupled MNPs and is beneficial to relevant applications.

Characterizing Superradiant Phase of the Quantum Rabi Model

Recently, a superradiant phase transition first predicted theoretically in the quantum Rabi model (QRM) has been verified experimentally. This further stimulates the interest in the study of the process of phase transition and the nature of the superradiant phase since the fundamental role of the QRM in describing the interaction of light and matter, and more importantly, the QRM contains rich physics deserving further exploration despite its simplicity. Here we propose a scheme consisting of two successive diagonalizations to accurately obtain the ground-state and excited states wavefunctions of the QRM in full parameter regime ranging from weak to deep-strong couplings. Thus, one is able to see how the phase transition occurs and how the photons populate in Fock space of the superradiant phase. We characterize the photon populations by borrowing the distribution concept in random matrix theory and find that the photon population follows a Poissonian-like distribution once the phase transition takes place and further exhibits the statistics of Gaussian unitary ensemble with increasing coupling strength. More interestingly, the photons in the excited states behave even like the statistics of Gaussian orthogonal ensemble. Our results not only deepen understanding on the superradiant phase transition but also provide an insight on the nature of the superradiant phase of the QRM and related models.

Light-responsive organic polaritons from first principles.

Controlling the optical properties of light-responsive organic molecules is essential for their application in photonics. We demonstrate how light-responsive organic polaritons formed inside an optical cavity can be used to modify these properties based on first principles. Specifically, we study the excited state properties of the trans-azobenzene molecule and the free base tetraphenyl porphyrin (H2TPP) molecule under weak to strong light-matter coupling. Our results show that the cavity can modulate the dispersion and absorption properties of organic molecules. Compared to the case outside the cavity, the anomalous dispersion of the trans-azobenzene molecule inside the cavity is suppressed and this suppression decreases with increasing coupling strength, showing the potential of strong light-matter coupling in manipulating the optical dipole trap of organic molecules. Moreover, by adjusting the cavity parameters to tune the strength of the light-matter coupling, we achieve free switching between symmetric Lorentz and asymmetric Fano line shapes for H2TPP polaritonic excitations. During the switching between these spectral features, we also find that the cavity can be used to control the spontaneous radiation of organic molecules via the Purcell effect. These findings provide a new pathway to manipulate the optical properties of light-responsive organic molecules.

Versatile Tunable Microresonator for the Light-Matter Interaction Studying in the Strong-Coupling Mode

The interaction between an ensemble of molecules and an electromagnetic field in a highly limited volume makes it possible to control the properties of a substance and, therefore, is an exceptionally promising area of research. The most common way to achieve weak or strong light-matter coupling is to place an ensemble of molecules in a micron-sized resonator. In such a system,the interaction of light with matter appears in the form of a change in the spectral response of the system, which depends on the strength of the coupling between the ensemble of molecules and the modes of the resonator. Currently, there is no general and user-friendly approach that allows studying a lot of different samples in a wide optical range using the same resonator setup. The present paper describes the design of a device that makes it possible to overcome this disadvantage, speed up and facilitate the study of the light-matter interaction, and also obtain weak and strong light-matter coupling modes for a large number of samples in the UV, visible, and IR regions of the optical spectrum. The device developed here is based on the tunable unstable λ/2 Fabry-Perot microresonator, consisting of flat and convex mirrors, which satisfy the condition of plane-parallelism at least at one point of the curved mirror and can significantly reduce the mode volume. The device was used to study the effect of the strong-coupling regime on the fluorescent properties of the Rhodamine 6G (R6G) dye embedded in a boron nitride nanoparticles matrix. It was found that the use of boron nitride (h-BN) as a carrier matrix has an orienting effect on the dye molecules, that results in an increase of the light-matter coupling strength at a lower resonator mode energy required. Keywords: microspectroscopy, optical microresonator, strong coupling, boron nitride.

Tuning nanoscale plasmon-exciton coupling via chemical interface damping.

Understanding the exact role of each plasmon decay channel in the plasmon-exciton interaction is essential for realizing the translational potential of nanoscale plexciton hybrids. Here, using single-particle spectroscopy, we demonstrate how a particular decay channel, chemical interface damping (CID), influences the nanoscale plasmon-exciton coupling. We investigate the interaction between cyanine dye J-aggregates and gold nanorods in the presence and absence of CID. The CID effect is introduced via surface modification of the nanorods with 4-nitrothiophenol. The relative contribution of CID is systematically tuned by varying the diameter of the nanorods, while maintaining the aspect ratio constant. We show that the incorporation of the CID channel, in addition to other plasmon decay channels, reduces the plasmon-exciton coupling strength. Nanorods' diameter-dependency measurements reveal that in the absence of CID contribution, the plasmon mode-volume factor gradually dominates over the plasmon decoherence effects as the diameter of the nanorods decreases, resulting in an increase in the plasmon-exciton coupling strength. However, the situation is entirely different when the CID channel is active: plasmon dephasing determines the plasmon-exciton coupling strength by outweighing the influence of even a very small plasmon mode-volume. Most importantly, our findings indicate that CID can be used to controllably tune the plasmon-exciton coupling strength for a given plexciton system by modifying the nanoparticle's surface with suitable adsorbates without the need for altering either the plasmonic or excitonic systems. Thus, judicious exploitation of CID can be tremendously beneficial in tailoring the optical characteristics of plexciton hybrid systems to suit any targeted application.

Универсальный перестраиваемый микрорезонатор для исследования взаимодействия света с веществом в ржиме сильной связи

The interaction between an ensemble of molecules and an electromagnetic field in a highly limited volume makes it possible to control the properties of a substance and, therefore, is an exceptionally promising area of research. The most common way to achieve weak or strong light-matter coupling is to place an ensemble of molecules in a micron-sized resonator. In such a system,the interaction of light with matter appears in the form of a change in the spectral response of the system, which depends on the strength of the coupling between the ensemble of molecules and the modes of the resonator. Currently, there is no general and user-friendly approach that allows studying a lot of different samples in a wide optical range using the same resonator setup. The present paper describes the design of a device that makes it possible to overcome this disadvantage, speed up and facilitate the study of the light-matter interaction, and also obtain weak and strong light-matter coupling modes for a large number of samples in the UV, visible, and IR regions of the optical spectrum. The device developed here is based on the tunable unstable λ/2 Fabry-Perot microresonator, consisting of flat and convex mirrors, which satisfy the condition of plane-parallelism at least at one point of the curved mirror and can significantly reduce the mode volume. The device was used to study the effect of the strong-coupling regime on the fluorescent properties of the Rhodamine 6G (R6G) dye embedded in a boron nitride nanoparticles matrix. It was found that the use of boron nitride (h-BN) as a carrier matrix has an orienting effect on the dye molecules, that results in an increase of the light-matter coupling strength at a lower resonator mode energy required.

Robustness of Interdependent Networks with Weak Dependency Based on Bond Percolation.

Real-world systems interact with one another via dependency connectivities. Dependency connectivities make systems less robust because failures may spread iteratively among systems via dependency links. Most previous studies have assumed that two nodes connected by a dependency link are strongly dependent on each other; that is, if one node fails, its dependent partner would also immediately fail. However, in many real scenarios, nodes from different networks may be weakly dependent, and links may fail instead of nodes. How interdependent networks with weak dependency react to link failures remains unknown. In this paper, we build a model of fully interdependent networks with weak dependency and define a parameter α in order to describe the node-coupling strength. If a node fails, its dependent partner has a probability of failing of 1-α. Then, we develop an analytical tool for analyzing the robustness of interdependent networks with weak dependency under link failures, with which we can accurately predict the system robustness when 1-p fractions of links are randomly removed. We find that as the node coupling strength increases, interdependent networks show a discontinuous phase transition when α<αc and a continuous phase transition when α>αc. Compared to site percolation with nodes being attacked, the crossover points αc are larger in the bond percolation with links being attacked. This finding can give us some suggestions for designing and protecting systems in which link failures can happen.

Quantum thermometry with a dissipative quantum Rabi system

Dissipative quantum Rabi system, a finite-component system composed of a single two-level atom interacting with an optical cavity field mode, exhibits a quantum phase transition, which can be exploited to greatly enhance the estimation precision of unitary parameters (frequency and coupling strength). Here, using the quantum Langevin equation, standard mean field theory and adiabatic elimination, we investigate the quantum thermometry of a thermal bath surrounding the atom with quantum optical probes. With the increase in coupling strength between the atom and the cavity field, two kinds of singularities can be observed. One type of singularity is the critical point (CP) of phase transition from the normal to superradiant phase. The other type of singularity is the exceptional point (EP) in the anti-parity-time (anti-\(\mathcal{P}\mathcal{T}\)) symmetrical cavity field. In many previous jobs, the optimal measurement precision can appear around EPs. However, we show that the optimal measurement precision occurs at the CP, instead of the EP. And the direct photon detection represents an excellent proxy for the optimal measurement near the CP. In the case where the thermal bath to be tested is independent of the extra thermal bath interacting with the cavity field, the estimation precision of the temperature always increases with the coupling strength. Oppositely, if the thermal bath to be tested is in equilibrium with the extra thermal bath interacting with the cavity field, noises that suppress the information of the temperature will be introduced when increasing the coupling strength unless it is close to the CP.

Dynamical Mechanism Analysis of Three Neuroregulatory Strategies on the Modulation of Seizures.

This paper attempts to explore and compare the regulatory mechanisms of optogenetic stimulation (OS), deep brain stimulation (DBS) and electromagnetic induction on epilepsy. Based on the Wilson-Cowan model, we first demonstrate that the external input received by excitatory and inhibitory neural populations can induce rich dynamic bifurcation behaviors such as Hopf bifurcation, and make the system exhibit epileptic and normal states. Then, both OS and DBS are shown to be effective in controlling the epileptic state to a normal low-level state, and the stimulus parameters have a broad effective range. However, electromagnetic induction cannot directly control epilepsy to this desired state, even if it can significantly reduce the oscillation frequency of neural populations. One main difference worth noting is that the high spatiotemporal specificity of OS allows it to target inhibitory neuronal populations, whereas DBS and electromagnetic induction can only stimulate excitatory as well as inhibitory neuronal populations together. Next, the propagation behavior of epilepsy is explored under a typical three-node feedback loop structure. An increase in coupling strength accelerates and exacerbates epileptic activity in other brain regions. Finally, OS and DBS applied to the epileptic focus play similar positive roles in controlling the behavior of the area of seizure propagation, while electromagnetic induction still only achieves unsatisfactory effects. It is hoped that these dynamical results can provide insights into the treatment of epilepsy as well as other neurological disorders.

Graphene/Cs2PbI2Cl2 van der Waals heterostructure with tunable Schottky barriers and contact types

Two-dimensional halide perovskite Cs2PbI2Cl2 with the Ruddlesden–Popper structure has attracted much interest in both experiment and theory, owing to its excellent structural stability and electronic and optical properties. Here, we design the graphene/Cs2PbI2Cl2 van der Waals (vdW) heterostructure (HS) and comprehensively investigate its structural, electronic, and contact properties by using first principle calculations. Four types of graphene/Cs2PbI2Cl2 HSs are considered, and the most stable one is identified. Because the composed system has weak vdW interaction, the intrinsic band structures of both graphene and Cs2PbI2Cl2 are well maintained. Meanwhile, the graphene opens a minute energy gap of about 68 meV, which may have resulted from a broken sublattice inversion symmetry and tiny structure distortion. Moreover, it is found that graphene/Cs2PbI2Cl2 forms a p-type Schottky contact. The HS undergoes a contact-type transition to p-type Ohmic contact and n-type Ohmic contact from the original p-type Schottky contact under positive and negative electric fields, respectively. When interlayer coupling strength increases or decreases, a contact-type transition to the p-type Ohmic contact from the original p-type Schottky contact occurs. These findings provide a meaningful guidance for tuning the electronic properties and constructing high-performance graphene/Cs2PbI2Cl2 HS-based Schottky devices.

On the spatial spread of active control in a van der Pol ring via synchronisation and its stabilisation using parameter mismatch

This work explores spatial propagation of amplitude control in a network of self-excited oscillators having ring topology. We consider a ring of N Van der Pol oscillators, with a first order control model connected to an arbitrary kth oscillator in the network. It is shown that even such a simple one-dimensional control, applied to the kth oscillator, can be made to propagate to other oscillators due to the synchronising property of the network, bringing about the control of their amplitudes also. The slow flow equations of amplitude and phase of the complete model, obtained analytically, are used to study the spatial propagation of control in the network. The oscillator responses are approximated by quasi-harmonic functions whereas the first order control response is approximated by the superposition of relaxation and oscillatory terms. The obtained analytical approximations are validated by comparing them with numerical simulation. The effect of the synchronising property of the network on the spread of amplitude control is investigated and it is shown that the extent and speed of amplitude control increases with increase in coupling strength. It is further shown that the control strategy is not effective when the control gain parameter is greater than the square of linear natural frequency of the oscillator (γ>ωk2). We propose the use of parameter mismatch between oscillators as a tool for overcoming this limitation. Frequency detuning, brought about by parameter mismatch, is shown to stabilise the fixed point at the origin and cause amplitude control even outside the effective range of the control mechanism. This shows that slight differences between the oscillators, unavoidable during manufacturing, can be beneficial for the spatial spread of control in the network.