Multistable 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.

The Effect of Indian Ocean Surface Freshwater Flux Biases On the Multi-Stable Regime of the AMOC

The Effect of Indian Ocean Surface Freshwater Flux Biases On the Multi-Stable Regime of the AMOC

A taxonomy of multiple stable states in complex ecological communities.

Natural systems are built from multiple interconnected units, making their dynamics, functioning and fragility notoriously hard to predict. A fragility scenario of particular relevance concerns so-called regime shifts: abrupt transitions from healthy to degraded ecosystem states. An explanation for these shifts is that they arise as transitions between alternative stable states, a process that is well-understood in few-species models. However, how multistability upscales with system complexity remains a debated question. Here, we identify that four different multistability regimes generically emerge in models of species-rich communities and other archetypical complex biological systems assuming random interactions. Across the studied models, each regime consistently emerges under a specific interaction scheme and leaves a distinct set of fingerprints in terms of the number of observed states, their species richness and their response to perturbations. Our results help clarify the conditions and types of multistability that can be expected to occur in complex ecological communities.

Neural heterogeneity controls computations in spiking neural networks.

The brain is composed of complex networks of interacting neurons that express considerable heterogeneity in their physiology and spiking characteristics. How does this neural heterogeneity influence macroscopic neural dynamics, and how might it contribute to neural computation? In this work, we use a mean-field model to investigate computation in heterogeneous neural networks, by studying how the heterogeneity of cell spiking thresholds affects three key computational functions of a neural population: the gating, encoding, and decoding of neural signals. Our results suggest that heterogeneity serves different computational functions in different cell types. In inhibitory interneurons, varying the degree of spike threshold heterogeneity allows them to gate the propagation of neural signals in a reciprocally coupled excitatory population. Whereas homogeneous interneurons impose synchronized dynamics that narrow the dynamic repertoire of the excitatory neurons, heterogeneous interneurons act as an inhibitory offset while preserving excitatory neuron function. Spike threshold heterogeneity also controls the entrainment properties of neural networks to periodic input, thus affecting the temporal gating of synaptic inputs. Among excitatory neurons, heterogeneity increases the dimensionality of neural dynamics, improving the network's capacity to perform decoding tasks. Conversely, homogeneous networks suffer in their capacity for function generation, but excel at encoding signals via multistable dynamic regimes. Drawing from these findings, we propose intra-cell-type heterogeneity as a mechanism for sculpting the computational properties of local circuits of excitatory and inhibitory spiking neurons, permitting the same canonical microcircuit to be tuned for diverse computational tasks.

Dual-microcomb generation via a monochromatically pumped dual-mode microresonator

Microcombs have enabled a host of cutting-edge applications from metrology to communications that have garnered significant attention in the last decade. Nevertheless, due to the thermal instability of the microresonator, additional control devices like auxiliary lasers are indispensable for single-soliton generation in some scenarios. Specifically, the increased system complexity would be too overwhelming for dual-microcomb generation. Here, we put forward a novel approach to mitigate the thermal instability and generate the dual-microcomb using a compact system. This process is akin to mode-division multiplexing, as the dual-microcombs are generated by pumping the dual-mode of a single Si3N4 microresonator with a continuous-wave laser. Both numerical simulations and experimental measurements indicate that this innovative technique could offer a straightforward way to enlarge the soliton existence range, allowing entry into the multistability regime and triggering another microcomb alongside the main soliton pulse. This outcome not only shines new light on the interaction mechanism of microresonator modes but also provides an avenue for the development of dual-microcomb-based ranging and low phase noise microwave generation.

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.

Modeling of dual frequency combs and bistable solitons in third-harmonic generation

Phase-matching of the third-harmonic generation process can be used to extend the emission of radiation from Kerr microresonators into new spectral regions far from the pump wavelength. Here, we present a theoretical mean-field model for optical frequency combs in a dissipative and nonlinear χ(3)-based cavity system with parametric coupling between fundamental and third-harmonic waves. We investigate temporally dispersive dual-comb generation of phase-matched combs with broad bandwidth and anomalous dispersion of the fundamental field, individuating conditions for accessing a multistable regime that simultaneously supports two types of coupled bright cavity solitons. These bistable cavity solitons coexist for the same pump power and frequency detuning, while featuring dissimilar amplitudes of their individual field components. Third-harmonic generation frequency combs grant telecom pump laser sources a simultaneous and direct access to both the near-infrared and the visible regions, which may prove advantageous for the development of optical clocks and sensing applications.

Continuous and explosive synchronization of phase oscillators on star network: Effect of degree-frequency correlations and time-delays

It is crucial to find time-delay intervals that control and mediate the onset and suppression of explosive synchronization in complex systems. To address this, we study the desynchrony-to-synchrony transitions in delay-coupled phase oscillators with degree-frequency correlation on a star network. We study how delay affects the transitions from desynchrony to synchrony. We observe that the system first undergo remote synchronization and the routes to synchrony are either continuous or discontinuous, depending on the delay intervals. We provide numerical results to establish a fundamental relation between delay intervals and time-period induced by the system’s average frequency of intrinsic oscillators. In the regime of global synchrony, all oscillators operate with a common frequency, and a phase shift develops between the hub and peripheral oscillators. We derive the analytical expression of common frequency, the phase difference between oscillators, and the threshold coupling strength for the onset of global synchronization. We perform a linear stability analysis of the common frequency at the point of threshold coupling and examine the series of saddle–node bifurcations present in the system. Estimates of linearly stable solutions of frequency are found to be in good agreement with numerical results. Hence, this study elucidates the role of delay on the routes to synchrony, stability of synchronization solutions, and multistability regimes.

Merging and disconnecting resonance tongues in a pulsing excitable microlaser with delayed optical feedback.

Excitability, encountered in numerous fields from biology to neurosciences and optics, is a general phenomenon characterized by an all-or-none response of a system to an external perturbation of a given strength. When subject to delayed feedback, excitable systems can sustain multistable pulsing regimes, which are either regular or irregular time sequences of pulses reappearing every delay time. Here, we investigate an excitable microlaser subject to delayed optical feedback and study the emergence of complex pulsing dynamics, including periodic, quasiperiodic, and irregular pulsing regimes. This work is motivated by experimental observations showing these different types of pulsing dynamics. A suitable mathematical model, written as a system of delay differential equations, is investigated through an in-depth bifurcation analysis. We demonstrate that resonance tongues play a key role in the emergence of complex dynamics, including non-equidistant periodic pulsing solutions and chaotic pulsing. The structure of resonance tongues is shown to depend very sensitively on the pump parameter. Successive saddle transitions of bounding saddle-node bifurcations constitute a merging process that results in unexpectedly large regions of locked dynamics, which subsequently disconnect from the relevant torus bifurcation curve; the existence of such unconnected regions of periodic pulsing is in excellent agreement with experimental observations. As we show, the transition to unconnected resonance regions is due to a general mechanism: the interaction of resonance tongues locally at an extremum of the rotation number on a torus bifurcation curve. We present and illustrate the two generic cases of disconnecting and disappearing resonance tongues. Moreover, we show how a pair of a maximum and a minimum of the rotation number appears naturally when two curves of torus bifurcation undergo a saddle transition (where they connect differently).

Offset parameter cancellation produces countless coexisting attractors.

The average value of a system variable determines the position of its attractor. When the offset parameters come together and get disappeared after an algebraic operation, the location of the attractor is then governed by an initial condition only. In this case, parameter-dominated offset control turns out to be the initial condition-defined coexisting attractors. In this Letter, a special mechanism for generating countless coexisting attractors is disclosed. Furthermore, a new regime of multistability is revealed, which explains where and how countless coexisting attractors are born and arranged.

Nonclassical correlated optical multistability at low photon level for cavity electromagnetically induced transparency

We study the nonequilibrium dynamic behaviors in a driven-dissipative single-atom cavity electromagnetically induced transparency. The optical bistability and multistability beyond a Kerr nonlinearity are observed utilizing the optical Stark shift induced strong nonlinearity. We show that the nonequilibrium dynamical phase transition between bistability and multistability is highly tunable by the system parameters in a large parameter region. The first-order dissipative optical bistability (multistability) always corresponds to the photon-bunching quantum statistics, which indicates that the quantum fluctuations and correlations play important roles in nonequilibrium dynamics. Interestingly, bistability and multistability with photon-bunching quantum statistics occurring at extremely low steady-state cavity photon number are observed, even under a very strong cavity driven field. Furthermore, we demonstrate that the unique cavity steady-state solution of the full quantum calculation is excellently consistent with the lowest solution based on the semiclassical mean-field approach in bistability and multistability regimes when the cavity photon number is much less than unity, albeit these nonclassical quantum states should possess strong quantum fluctuations in this parameter regime. Our results pave the way to exploring nonclassical correlated optical multistability in quantum regime, which may bring exciting opportunities for potential applications from quantum information processing to quantum metrology.

Voltage-driven multistability and chaos in magnetic films

The control of magnetization dynamics has allowed numerous technological applications. Magnetization dynamics can be excited by, e.g., alternating magnetic fields, charge and spin currents, and a voltage-induced control of interfacial properties. An example of the last mechanism is the voltage-controlled magnetic anisotropy effect, which can induce magnetization precessions and switchings with low-power consumption. Time-dependent voltage-controlled magnetic anisotropy can induce complex dynamic behaviors for magnetization. This work studies the magnetization dynamics of a single magnetic nano-oscillator forced with a time-dependent voltage-controlled magnetic anisotropy. Unexpectedly, the oscillator displays multistable regimes, i.e., distinct initial conditions evolve towards different oscillatory states. When voltage is changed the oscillatory state exhibits period-doubling route to chaos. The chaotic behavior is numerically demonstrated by the determination of the largest Lyapunov exponent.

Spin oscillations of a single-mode polariton system driven by a plane wave

Theoretical study is performed of a single-mode polariton system with linear coupling of spin components. When combined with an ordinary two-particle interaction, the spin coupling involves a spontaneous symmetry breaking accompanied by a switch from linear to circular polarization under resonant driving. The asymmetric steady states can also lose stability, giving way to oscillatory and chaotic dynamics. Here, we explore a continuous transformation between the multistable regime, where the system is steady and locked in phase to the pump but has a broken spin symmetry, and full-span oscillations of the circular-polarization degree, owing to which the symmetry is effectively reestablished. Such oscillations are analogous to the intrinsic Josephson effect and prove to be robust against arbitrarily strong perturbations. Transitional phenomena include the Hopf bifurcation, spin bistability of limit cycles, and continuous transitions to and from dynamical chaos through series of period doubling/halving events.

Electrotuneable Radical Polymers for Thin-Film Electronic Device Applications

Polyradicals – organic radical polymers in which each repeating unit contains a singly occupied molecular orbital (i.e. an unpaired electron spin) – are unique alternatives to their π-conjugated and semiconducting counterparts for several applications.[1] Unique of polyradicals are tunable charge states at their repeating units (see figure) which enable multi-stable charge transport regimes at the nanoscale. In this talk, we will present the use of thin films of polyradicals in transparent and flexible thin-film nanoelectronics. Although field-effect thin-film transistors (FETs) and flash memory devices ("memristors") based on radical polymers have been often proposed, memristor stability was frequently limited to a few writing cycles, in spite of the excellent quality of the active layer, and no FETs have been demonstrated, even though evidence of polyradical doping has been offered.[2]Here, the design criteria for flash memory devices are reviewed.It will be shown, using a combination of Kelvin-probe force microscopy (KPFM), electrical transport and optical measurements, that single-layer flash memory devices can be demonstrated from 6-oxoverdazyls, a class of radical polymers from which ultra-thin and ultra-smooth organic thin flims are advantageously processable.[3] As a case study, ultrathin devices in which the active layer is formed by a 15-nm homogeneous film of a poly-norbornene-6-oxoverdazyl (PN-6OV) polyradical synthesized by a dry vacuum polymer deposition technique are presented and compared with the corresponding devices of poly-6-oxoverdazyls (P6OV) synthesized by wet chemistry. [4] We will show that high performance is associated to the presence three tunable charge states in each monomer: positive, neutral, and negative, and also depends on the length of the pendant groups to which the radical repeating units are attached. We will demonstrate that careful engineering of the anode and cathode work functions, specifically aligning them with the negative and positive energy levels of the polyradical, is vital to maximize the on/off current ratio and ensure flash operation. The possibility to achieve electro-tunable poly-6-oxoverdazyl radical polymers by different techniques offer uniques opportunities for their use in a variety of different contexts, for example in transparent and/or flexible electronics, and where compatibility with different substrates is required.In the last part of our talk, we will present how a vertical device architecture, with drain-source contacts sandwiching the active layer of a strongly correlated 6-oxoverdazyl polyradical, leads to on/off ratios >103 in p-type PR-FETs. [4] Hole injection thus occurs by contact doping via tunable charge states at the polyradical-electrode interface. PRFETs are superior to existing organic FETs as they combine memristor and transistor functions in one mem-transistor device, offering unique potential for synaptic and spintronic applications.[1] Joo, Y.; Agarkar, V.; Sung, S. H.; Savoie, B. M.; Boudouris, B. W. A Nonconjugated Radical Polymer Glass with High Electrical Conductivity. Science 2018, 359, 1391-1395[2] Nguyen, T. P.; Easley, A. D.; Kang, N.; Khan, S.; Lim,S-M.; Rezenom, Y. H.; Wang, S.; Tran, D. K.; Fan, J.; Letteri, R. A.; He, X.; Su, L.; Yu, C-H.; Lutkenhaus, J. L.; Wooley K, L. Polypeptide organic radical batteries. Nature, 2021, 593, 61[3] Ezugwu, S.; Paquette, J. A.; Yadav, V.; Gilroy, J. B.; Fanchini, G. Design Criteria for Ultrathin Single-Layer Flash Memristors from an Organic Polyradical. Adv. Electron. Mater. 2016, 2, 1600253[4] Singh, D.; Magnan, F.; Gilroy, J. B.; Fanchini, G. Transparent and flexible field-effect transistors and mem-transistors with electroactive layers of solution-processed organic polyradicals, https://arxiv.org/abs/1910.10212 Figure 1

Central pattern generator based on self-sustained oscillator coupled to a chain of oscillatory circuits.

We have proposed and studied both numerically and experimentally a multistable system based on a self-sustained Van der Pol oscillator coupled to passive oscillatory circuits. The number of passive oscillators determines the number of multistable oscillatory regimes coexisting in the proposed system. It is shown that our system can be used in robotics applications as a simple model for a central pattern generator (CPG). In this case, the amplitude and phase relations between the active and passive oscillators control a gait, which can be adjusted by changing the system control parameters. Variation of the active oscillator's natural frequency leads to hard switching between the regimes characterized by different phase shifts between the oscillators. In contrast, the external forcing can change the frequency and amplitudes of oscillations, preserving the phase shifts. Therefore, the frequency of the external signal can serve as a control parameter of the model regime and realize a feedback in the proposed CPG depending on the environmental conditions. In particular, it allows one to switch the regime and change the velocity of the robot's gate and tune the gait to the environment. We have also shown that the studied oscillatory regimes in the proposed system are robust and not affected by external noise or fluctuations of the system parameters. Moreover, using the proposed scheme, we simulated the type of bipedal locomotion, including walking and running.

Periodic offset boosting for attractor self-reproducing.

The special regime of multistability of attractor self-reproducing is deeply decoded based on the conception of offset boosting in this letter. Attractor self-reproducing is essentially originated from periodic initial condition-triggered offset boosting. Typically, a trigonometric function is applied for attractor self-reproducing. The position, size, and clone frequency determine the selected periodic function. Specifically, in-depth investigation on three elements of sinusoidal quantity is taken into account and then a universal law of attractor self-reproducing is built: the original position of an attractor determines the initial phase and the size of attractor sets the amplitude, while the reproducing interval between two attractors determines the frequency of the trigonometric function. It is found that the product of amplitude and frequency is a constant determined by the reproducing periodic function. The positive and negative switching of the slope in sinusoidal function also leads to the waste of phase space since in general there is no attractor reproduced at the region with negative slope except that new polarity balance is reconstructed paying back the attractor with conditional symmetry. Three-element-oriented offset boosting makes attractor self-reproducing more designable, achievable, and adjustable, which brings great convenience to engineering applications.

Asymmetry Evolvement and Controllability of a Symmetric Hyperchaotic Map

Trigonometric functions were used to construct a 2-D symmetrical hyperchaotic map with infinitely many attractors. The regime of multistability depends on the periodicity of the trigonometric function, which is closely related to the initial condition. For this trigonometric nonlinearity and the introduction of an offset controller, the initial condition triggers a specific multistability evolvement, in which infinitely countless symmetric and asymmetric attractors are produced. Initial condition-triggered offset boosting is explored, combined with constant controlled offset regulation. Furthermore, this symmetric map gives the sequences in various types of asymmetric attractors, in which the polarity balance is maintained by the initial condition and a negative coefficient due to the trigonometric function. Finally, as determined through the hardware implementation of STM32, the corresponding results agree with the numerical simulation.

Bursting and Excitability in Neuromorphic Resonant Tunneling Diodes

We study in this paper the dynamics of quantum nanoelectronic resonant tunneling diodes (RTDs) as excitable neuromorphic spike generators. We disclose the mechanisms by which the RTD creates excitable all-or-nothing spikes and we identify a regime of bursting in which the RTD emits a random number of closely packed spikes. The control of the latter is paramount for applications in event-activated neuromorphic sensing and computing. Finally, we discuss a regime of multi-stability in which the RTD behaves as a memory. Our results can be extended to other devices exhibiting negative differential conductance.

Emergence of multistability and strongly asymmetric collective modes in two quorum sensing coupled identical ring oscillators.

The simplest ring oscillator is made from three strongly nonlinear elements repressing each other unidirectionally, resulting in the emergence of a limit cycle. A popular implementation of this scheme uses repressor genes in bacteria, creating the synthetic genetic oscillator known as the Repressilator. We consider the main collective modes produced when two identical Repressilators are mean-field-coupled via the quorum-sensing mechanism. In-phase and anti-phase oscillations of the coupled oscillators emerge from two Andronov-Hopf bifurcations of the homogeneous steady state. Using the rate of the repressor's production and the value of coupling strength as the bifurcation parameters, we performed one-parameter continuations of limit cycles and two-parameter continuations of their bifurcations to show how bifurcations of the in-phase and anti-phase oscillations influence the dynamical behaviors for this system. Pitchfork bifurcation of the unstable in-phase cycle leads to the creation of novel inhomogeneous limit cycles with very different amplitudes, in contrast to the well-known asymmetrical limit cycles arising from oscillation death. The Neimark-Sacker bifurcation of the anti-phase cycle determines the border of an island in two-parameter space containing almost all the interesting regimes including the set of resonant limit cycles, the area with stable inhomogeneous cycle, and very large areas with chaotic regimes resulting from torus destruction and period doubling of resonant cycles and inhomogeneous cycles. We discuss the structure of the chaos skeleton to show the role of inhomogeneous cycles in its formation. Many regions of multistability and transitions between regimes are presented. These results provide new insights into the coupling-dependent mechanisms of multistability and collective regime symmetry breaking in populations of identical multidimensional oscillators.

Nonlinear frequency response of the multi-resonant ring cavities

A convenient for practical use new theoretical approach describing a nonlinear frequency response of the multi-resonant nonlinear ring cavities (RC) to an intense monochromatic wave action is developed. The approach closely relates the many-valuednesses of the RC frequency response and the dispersion relation of a waveguide, from which the cavity is produced. Arising of the multistability regime in the nonlinear RC is treated. The threshold and the dynamic range of the bistability and tristability regimes for an optical ring cavity with the Kerr nonlinearity are derived and discussed.