Bistable Regime Research Articles

Excitation and manipulation of super cavity solitons in multi-stable passive Kerr resonators

We report on the theoretical analysis as well as the numerical simulations about the nonlinear dynamics of cavity solitons in a passive Kerr resonator operating in the multistable regime under the condition of a sufficiently strong pump. In this regime, the adjacent tilted cavity resonances might overlap, thus leading to the co-existence of combinatory states of temporal cavity solitons and the extended modulation instability patterns. The cavity in the regime of multistablity may sustain distinct families of cavity solitons, vividly termed as super cavity solitons with much higher intensity and broader spectra if compared with those in the conventional bi-stable regime. The description of such complex cavity dynamics in the multstable regime requires either the infinite-dimensional Ikeda map, or the derived mean-field coupled Lugiato-Lefever equations by involving multiple contributing cavity resonances. With the latter model, we revealed the existence of different orders of super cavity solitons, whose stationary solutions were obtained by using the Newton-Raphson algorithm. Along this line, with the continuation calculation, we have plotted the Hopf / saddle-node bifurcation curves, thus identifying the existing map of the stable and breathing (super) cavity solitons. With this defined parameter space, we have proposed an efficient method to excite and switch the super cavity solitons by adding an appropriate intensity (or phase) perturbation on the pump. Such deterministic cavity soliton manipulation technique is demonstrated to underpin the multi-level coding, which may enable the large capacity all-optical buffering based on the passive fiber ring cavities.

Emergence of subharmonics in a microwave driven dissipative Rydberg gas

Quantum many-body systems near phase transitions respond collectively to externally applied perturbations. We explore this phenomenon in a laser-driven dissipative Rydberg gas that is tuned to a bistable regime. Here two metastable phases coexist, which feature a low and high density of Rydberg atoms, respectively. The ensuing collective dynamics, which we monitor , is characterized by stochastic collective jumps between these two macroscopically distinct many-body phases. We show that the statistics of these jumps can be controlled using a dual-tone microwave field. In particular, we find that the distribution of jump times develops peaks corresponding to subharmonics of the relative microwave detuning. Our study demonstrates the control of collective statistical properties of dissipative quantum many-body systems without the necessity of fine-tuning or of ultracold temperatures. Such robust many-body phenomena may find technological applications in sensing. Published by the American Physical Society 2024

Numerical Exploration of a Network of Nonlocally Coupled Josephson Junction Spurred by Wien BridgeOscillators

This paper focuses on the numerical study of the collective dynamics of nonlocally coupled Josephson junctions (JJ) driven by Wien bridge oscillators (JJSWBOs). A single JJSWBO exhibits monostable and bistable chaotic behaviors, bistable period-3 oscillations, and a coexistence of regular and chaotic dynamics. To explore the network's collective dynamics, the local dynamics are set in a bistable regime, with initial conditions ensuring random distribution of units on these two types of behavior. Increasing the coupling strength transitions the network from complete incoherence to coherent traveling waves via a chimera state.

A Multi‐Data Set Analysis of the Freshwater Transport by the Atlantic Meridional Overturning Circulation at Nominally 34.5°S

AbstractThe freshwater transport (Mov) by the Atlantic Meridional Overturning Circulation (AMOC) across 34.5°S is computed using observations from 49 eXpendable BathyThermograph (XBT) transects between 2002 and 2019. The Mov at 34.5°S serves as a possible indicator of the AMOC stability, with a negative (southward) freshwater transport indicating a possible bistable AMOC regime and positive (northward) transport indicating a monostable regime. A negative Mov mean of −0.15 ± 0.09 Sv is estimated from the repeated XBT transects, suggesting a bistable AMOC regime. Results are complemented with two data sets derived from Argo float observations, numerical ocean models, and coupled climate models. More than half of the coupled models examined, 20 out of 32, present positive Mov mean values. To investigate the causes of the differing signs of the Mov across the models, we examine the salinity vertical structure in models with positive and negative Mov, indicating fresher upper and saltier deep waters in models with positive Mov. The South Atlantic meridional fluxes show linear relationships, with a negative slope (positively correlated in magnitude) between Mov/MOC and Mov/MHT, and a positive slope (positively correlated) between MHT/MOC. Seasonally, the South Atlantic meridional fluxes from most of the data sets considered here, show a more negative Mov and a more positive MOC and MHT in austral fall and winter from April to August across 34.5°S.

Growth of solitary slugs in long pipes

We show that a pipe transporting gas and liquid can be operated at conditions where both stratified flow and slug flow are stable. In this bi-stable flow regime, it is possible to observe stratified flow or regular hydrodynamic slug flow, depending on the inlet conditions. However, it is also possible to get one single slug at a time in the pipe. The distinctive characteristic of such “solitary” slugs is that they grow continuously as they travel along the pipe and therefore, in long pipelines, they can reach lengths up to thousands of pipe diameters and flood the downstream process installations. We first show how the length of solitary slugs can be predicted using slug tracking simulations. Based on those transient simulation results, we provide an explanation for the slug growth and we propose a simple quasi-steady-state model allowing us to predict the slug length in good agreement with the transient simulations. Finally, we explain how we can determine the boundaries of the bi-stable flow regime in which solitary slugs occur.

Harnessing sub-comb dynamics in a graphene-sensitized microresonator for gas detection

Since their inception, frequency combs generated in microresonators, known as microcombs, have sparked significant scientific interests. Among the various applications leveraging microcombs, soliton microcombs are often preferred due to their inherent mode-locking capability. However, this choice introduces additional system complexity because an initialization process is required. Meanwhile, despite the theoretical understanding of the dynamics of other comb states, their practical potential, particularly in applications like sensing where simplicity is valued, remains largely untapped. Here, we demonstrate controllable generation of sub-combs that bypasses the need for accessing bistable regime. And in a graphene-sensitized microresonator, the sub-comb heterodynes produce stable, accurate microwave signals for high-precision gas detection. By exploring the formation dynamics of sub-combs, we achieved 2 MHz harmonic comb-to-comb beat notes with a signal-to-noise ratio (SNR) greater than 50 dB and phase noise as low as − 82 dBc/Hz at 1 MHz offset. The graphene sensitization on the intracavity probes results in exceptional frequency responsiveness to the adsorption of gas molecules on the graphene of microcavity surface, enabling detect limits down to the parts per billion (ppb) level. This synergy between graphene and sub-comb formation dynamics in a microcavity structure showcases the feasibility of utilizing microcombs in an incoherent state prior to soliton locking. It may mark a significant step toward the development of easy-to-operate, systemically simple, compact, and high-performance photonic sensors.Graphical

Explosive Cooperation in Social Dilemmas on Higher-Order Networks.

Understanding how cooperative behaviors can emerge from competitive interactions is an open problem in biology and social sciences. While interactions are usually modeled as pairwise networks, the units of many real-world systems can also interact in groups of three or more. Here, we introduce a general framework to extend pairwise games to higher-order networks. By studying social dilemmas on hypergraphs with a tunable structure, we find an explosive transition to cooperation triggered by a critical number of higher-order games. The associated bistable regime implies that an initial critical mass of cooperators is also required for the emergence of prosocial behavior. Our results show that higher-order interactions provide a novel explanation for the survival of cooperation.

Nonlinearly induced entanglement in dissipatively coupled optomechanical system

Nonlinearly induced steady-state photon–phonon entanglement of a dissipative coupled system is studied in the bistable regime. Quantum dynamical characteristics are analysed by solving the mean-field and fluctuation equations of the system. It is shown that dissipative coupling can induce bistable behaviour for the effective dissipation of the system. Under suitable parameters, one of the steady states significantly reduces the dissipative effect of the system. Consequently, a larger steady-state entanglement can be achieved compared to linear dynamics. Furthermore, the experimental feasibility of the parameters is analysed. Our results provide a new perspective for the implementation of steady-state optomechanical entanglement.

On the dynamics and optimal control of a mathematical model of neuroblastoma and its treatment: Insights from a mathematical model

Celyvir is an advanced therapy medicine, consisting of mesenchymal stem cells (MSCs) containing the oncolytic virus ICOVIR 5. This paper sets out a dynamic system which attempts to capture the fundamental relationships between cancer, the immune system and adenoviruses. Two forms of treatment were studied: continuous and periodic, the second being closer to the real situation. In the analysis of the first model, in addition to identifying the critical points, their properties and bifurcation points, a number of numerical simulations were carried out. It has thus been shown that there are bistability regimes in which Celyvir can produce an equilibrium of tumor progression, or even freedom from tumor. A sensitivity analysis was also performed to determine which parameters are most important in the system. Subsequently, an optimal control problem with nonlinear objective functional has been formulated, where the therapeutic goal is not only to minimize the size of the tumor cell population and the total cost of treatment, but also to prevent the tumor from reaching a critical size. It has been shown that the optimal control is bang–bang. With the second model, a threshold value of viral load has been identified at which the success of the treatment could be ensured. It is clear in both models that a low viral load would lead to relapse of the disease. Finally, it is shown that a periodic bang–bang regime should be used to optimize treatment with Celyvir.

First Passage Times of Long Transient Dynamics in Ecology.

Long transient dynamics in ecological models are characterized by extended periods in one state or regime before an eventual, and often abrupt, transition. One mechanism leading to long transient dynamics is the presence of ghost attractors, states where system dynamics slow down and the system lingers before eventually transitioning to the true attractor. This transition results solely from system dynamics rather than external factors. This paper investigates the dynamics of a classical herbivore-grazer model with the potential for ghost attractors or alternative stable states. We propose an intuitive threshold for first passage time analysis applicable to both bistable and ghost attractor regimes. By formulating the first passage time problem as a backward Kolmogorov equation, we examine how the mean first passage time changes as parameters are varied from the ghost attractor regime to the bistable one, through a saddle-node bifurcation. Our results reveal that the mean and variance of first passage times vary smoothly across the bifurcation threshold, eliminating the deterministic distinction between ghost attractors and bistable regimes. This work suggests that first passage time analysis can be an informative way to classify the length of a long transient. A better understanding of the duration of long transients may contribute to greater ecological understanding and more effective environmental management.

Fast high-fidelity charge readout by operating a cavity-embedded Cooper-pair transistor in the Kerr bistable regime

Fast high-fidelity charge readout by operating a cavity-embedded Cooper-pair transistor in the Kerr bistable regime

Limits to predictability of the asymptotic state of the Atlantic Meridional Overturning Circulation in a conceptual climate model

Anticipating critical transitions in the Earth system is of great societal relevance, yet there may be intrinsic limitations to their predictability. For instance, the asymptotic state of a dynamical system possessing multiple chaotic attractors depends sensitively on the initial condition in the proximity of a fractal basin boundary. Here, we approach the problem of final-state sensitivity of the Atlantic Meridional Overturning Circulation (AMOC) using a conceptual climate model, composed of a slow bistable ocean coupled to a fast chaotic atmosphere. First, we explore the occurrence of long chaotic transients in the monostable regime, which can mask a loss of stability near bifurcations. In the bistable regime, we explicitly construct the chaotic saddle using the edge tracking technique. We quantify the final-state sensitivity through the maximum Lyapunov exponent and the lifetime of the saddle and find that the system exhibits a fractal basin boundary with almost full phase space dimension, implying vanishing predictability of the second kind near the basin boundary. Our results demonstrate the usefulness of studying non-attracting chaotic sets in the context of predicting climatic tipping points, and provide guidance for the interpretation of critical transitions in higher-dimensional climate models.

Role of hierarchical heterogeneity in shaping seizure onset dynamics: Insights from structurally-based whole-brain dynamical network models

The brain is a highly complex network system exhibiting nonlinear dynamics, and alterations in brain structure may give rise to pathological brain dynamics such as seizures. Recent efforts in whole-brain network modeling have provided a framework of integrating subject data with nonlinear dynamical models for reproducing empirically observed phenomenon. A question remaining largely unexplored is how the structure of brain network system support and affect seizure-like dynamics. In this paper, we simulate seizures using a structurally-based whole-brain dynamical model of coupled oscillators operating in the bistable regime, and seizure onset likelihood is quantified by the escape time for nodes to transit from background to oscillatory seizure state. Based on this model, the effect of spatial heterogeneity in brain regions on seizure onset dynamics is explored. Specifically, magnetic resonance imaging derived T1w/T2w myelin map is used to parameterize the model with biologically-relevant spatial heterogeneity that approximates structural hierarchy in the human cortex. The unique shaping effect of hierarchical heterogeneity on seizure onset dynamics is demonstrated through comparisons with surrogate models where the spatial order of heterogeneity is altered. We find that hierarchical heterogeneity could most effectively impede the propagation of excitation across brain networks. It may also improve the model’s capacity to better characterize latent seizure focus as observed clinically and to personalize for epilepsy patients. The robustness of results is demonstrated using an alternative way of representing spatial heterogeneity and a higher resolution of representing brain regions. Our findings highlight the significant role of hierarchical heterogeneity as a relevant mechanism of ictogenesis and its importance to be considered in the workflow of whole-brain modeling for epilepsy patients, which are fundamental to understanding the dynamical nature of the brain system and developing personalized treatments for epilepsy patients.

Mean exit times as global measure of resilience of tropical forest systems under climatic disturbances-Analytical and numerical results.

Both remotely sensed distribution of tree cover and models suggest three alternative stable vegetation states in the tropics: forest, savanna, and treeless states. Environmental fluctuation could cause critical transitions from the forest to the savanna state and quantifying the resilience of a given vegetation state is, therefore, crucial. While previous work has focused mostly on local stability concepts, we investigate here the mean exit time from a given basin of attraction, with partially absorbing and reflecting boundaries, as a global resilience measure. We provide detailed investigations using an established model for tropical tree cover with multistable precipitation regimes. We find that higher precipitation or weaker noise increases the mean exit time of the forest state and, thus, its resilience. Upon investigating the transition times from the forest state to other tree cover states, we find that in the bistable precipitation regime, the size of environmental fluctuations has a greater impact on the transition probabilities from the forest state compared to precipitation.

Prestrain-induced bistability in the design of tensegrity units for mechanical metamaterials

Tensegrity metamaterials are a type of artificial materials that can exploit the tunable nonlinear mechanical behavior of the constituent tensegrity units. Here, we present reduced-order analytical models describing the prestrain-induced bistable effect of two particular tensegrity units. Closed-form expressions of the critical prestrain at which a unit transitions into a bistable regime are derived. Such expressions depend only on the geometry of the units. The predictions of the reduced-order model are verified by numerical simulations and by the realization of physical models. The present results can be generalized to analogous units with polygonal base, and the proposed tensegrity units can be assembled together to form one-dimensional metamaterials with tailorable nonlinear features such as multistability and solitary wave propagation.

Detecting safe operational regimes of synchronous motor‐generator pair for wind integration: A non‐linear perspective

AbstractIn this article, the stability of a synchronous motor generator pair (SMGP) used for improving the inertia of grid‐connected renewable energy systems is investigated. The useful operational regime for different sets of system parameters is identified, such as electromagnetic torque, damping co‐efficient, and inertia by employing bifurcation analysis to detect stability boundaries. For the first time, the existence of bi‐stable regimes for the SMGP with non‐linear stability analysis is revealed. The authors' analysis unravels the possibility of the system getting transited to unsafe operation even when the system is in the linearly stable region. The existence of the bistable regime indicates the possibility of the system becoming unstable even when the eigenvalues are in the left half plane. The authors also identify globally stable and globally unstable regimes in the parameter space. The safe operating range of inertia and damping co‐efficient values helps in the design of a suitable MGP set that is robust to frequency deviations, even with a low inertia source. With the recommended values of electromagnetic torque, the authors' analysis provides a safe operational regime for power generation from renewable energy sources.

Mechanical cooling in the bistable regime of a dissipative optomechanical cavity with a Kerr medium

Mechanical cooling in the bistable regime of a dissipative optomechanical cavity with a Kerr medium

Reconfigurable all-optical bistability/tristability in dual injection-locked Fabry-Perot laser diodes.

In this Letter, we present a detailed theoretical and experimental investigation of optical bistability and tristability in dual injection-locked Fabry-Perot laser diodes. The proposed device can be reconfigured between the bistable and tristable regimes, simply by adjusting the power level of the injected control optical signal. The tristability presented in the experiment is achieved for relatively low optical input powers between 1.03 and 1.25 mW, with the output signal ratio of up to 7 dB between stable states. Such a device is a potential candidate for designing trits, a bit analogy in ternary computational logic.

Nonlinear optical switch based on coherent perfect absorption.

Coherent perfect absorption (CPA) or reflection (CPR) are methods to realize the extreme manipulation on an optical field. We propose a scheme to operate a bistable switch with convertible CPA and/or CPR. Generally, CPA and CPR occur with different input-field phases. For example, CPA is realized when two input probe beams are in phase; instead, CPR is achieved when they are out of phase. In this scheme, a CPA state can be converted to a CPR state by an incoherent field although two input fields are in phase. When we use the incoherent field as a switching field, the CPA (CPR) state is treated as the closed (open) state. As a result, the switching efficiency can theoretically reach a maximum value, i.e., η = 1. In addition, the switch can be operated in the linear regime with a weak input field, and in the nonlinear or bistable regime with a strong input field. Moreover, the efficiency of the bistable switch is sensitively dependent on the input-field intensity. It provides a potential application of this work on sensitive optical detecting.

On a bi-stability regime and the existence of odd subharmonics in a Comb-drive MEMS model with cubic stiffness

In this paper we study two different problems. First we present a novel result about the existence of a family of odd subharmonics with prescribed nodal properties for a general nonlinear oscillator with bounded domain and symmetries. Then we apply the general existence result to the Comb-drive finger MEMS model with a cubic nonlinear stiffness term, and prove analytically that the odd positive subharmonic of order two is linearly stable whenever the AC load of the input voltage is small enough. Moreover, we demonstrate a bi-stability regime for this model because the trivial solution x≡0 is also linearly stable. The general existence result was obtained through a generalization of the Ortega’s variational principle (Ortega, 2016), and the stability assertions were obtained by following the perturbation approach in Cen et al. (2020) for the linear stability of a nontrivial periodic solution that emanates from the autonomous problem, and the well-known Zukovskii criterion.