Rich Dynamics Research Articles

Parametric magnon transduction to spin qubits.

The integration of heterogeneous modular units for building large-scale quantum networks requires engineering mechanisms that allow suitable transduction of quantum information. Magnon-based transducers are especially attractive due to their wide range of interactions and rich nonlinear dynamics, but most of the work to date has focused on linear magnon transduction in the traditional system composed of yttrium iron garnet and diamond, two materials with difficult integrability into wafer-scale quantum circuits. In this work, we present a different approach by using wafer-compatible materials to engineer a hybrid transducer that exploits magnon nonlinearities in a magnetic microdisc to address quantum spin defects in silicon carbide. The resulting interaction scheme points to the unique transduction behavior that can be obtained when complementing quantum systems with nonlinear magnonics.

Localization, fractality, and ergodicity in a monitored qubit

We study the statistical properties of a single two-level system (qubit) subject to repetitive ancilla-based measurements. This setup is a fundamental minimal model for exploring the intricate interplay between the unitary dynamics of the system and the nonunitary stochasticity introduced by quantum measurements, which is central to the phenomenon of measurement-induced phase transitions. We demonstrate that this “toy model” harbors remarkably rich dynamics, manifesting in the distribution function of the qubit's quantum states in the long-time limit. We uncover a compelling analogy with the phenomenon of Anderson localization, albeit governed by distinct underlying mechanisms. Specifically, the state distribution function of the monitored qubit, parameterized by a single angle on the Bloch sphere, exhibits diverse types of behavior familiar from the theory of Anderson transitions, spanning from complete localization to almost uniform delocalization, with fractality occurring between the two limits. By combining analytical solutions for various special cases with two complementary numerical approaches, we achieve a comprehensive understanding of the structure delineating the “phase diagram” of the model. We categorize and quantify the emergent regimes and identify two distinct phases of the monitored qubit: ergodic and nonergodic. Furthermore, we identify a genuinely localized phase within the nonergodic phase, where the state distribution functions consist of delta peaks, as opposed to the delocalized phase characterized by extended distributions. Identification of these phases and demonstration of transitions between them in a monitored qubit are our main findings. Published by the American Physical Society 2024

Scale-to-scale energy flux in the oceanic global circulation models

Lewis Fry Richardson proposed his famous picture of turbulent flows in 1922, where the kinetic energy is transferred from large-scale to small-scale structures until the viscosity converts it into heat. This cascade idea, also known as the forward energy cascade, is now widely accepted and is treated as the cornerstone of not only turbulent modeling, but also global circulation models of the ocean and atmosphere. In this work, the Filter-Space-Technique is applied to the oceanic flow field provided by the CMEMS reanalysis model to quantify the scale-to-scale energy flux. A rich dynamical pattern associated with different scales is observed. More precisely, either positive or negative fluxes are observed, indicating the direction of the energy cascade, where the energy is transferred from large-scale structures to small-scale ones or vice versa. High-intensity energy exchange is found mainly in the Western Boundary Current Systems and Equatorial Counter Currents. For the latter case, a wavelike pattern is observed on the westward travel. Moreover, strong seasonal variation is evident for some scales and regions. These results confirm the existence of forward and inverse cascades and rich regional dynamics.

Co-dependent excitatory and inhibitory plasticity accounts for quick, stable and long-lasting memories in biological networks

The brain’s functionality is developed and maintained through synaptic plasticity. As synapses undergo plasticity, they also affect each other. The nature of such ‘co-dependency’ is difficult to disentangle experimentally, because multiple synapses must be monitored simultaneously. To help understand the experimentally observed phenomena, we introduce a framework that formalizes synaptic co-dependency between different connection types. The resulting model explains how inhibition can gate excitatory plasticity while neighboring excitatory–excitatory interactions determine the strength of long-term potentiation. Furthermore, we show how the interplay between excitatory and inhibitory synapses can account for the quick rise and long-term stability of a variety of synaptic weight profiles, such as orientation tuning and dendritic clustering of co-active synapses. In recurrent neuronal networks, co-dependent plasticity produces rich and stable motor cortex-like dynamics with high input sensitivity. Our results suggest an essential role for the neighborly synaptic interaction during learning, connecting micro-level physiology with network-wide phenomena.

A low-power artificial spiking neuron based on ionic memristor for modulated frequency coding

Neurons encode information through firing spikes with rich spatiotemporal dynamics. Using artificial neuron hardware based on memristors to emulate neuronal firing is of great significance for advancing the development of brain-like computing and artificial intelligence. However, it is still challenging to achieve low power frequency coding in memristive artificial neurons. Here, a low-power ionic memristor based on Pt/HfO2/Ag is reported for artificial spiking neurons. The device is driven by a low bias current and the filament dynamically ruptures and forms, producing oscillated voltage spikes that resemble neuronal spikes. The oscillation frequency increases from 0.5 Hz to ∼2.18 Hz with the stimulation current increasing from 1 nA to 5 nA, enabling the emulation of neuronal frequency-coding function. The low power consumption of ∼70 pJ per pulse indicates that the device is promising for energy-efficient neuromorphic computing applications. In addition, the device is found to be capable of simulating the phasic,adaptive, and burst firing modes of neurons.

Rich dynamics of a delayed Filippov avian-only influenza model with two-thresholds policy

A nonsmooth Filippov avian-only influenza model with threshold strategies of culling susceptible and/or infected birds under different conditions is proposed to control the spread of avian influenza. The time delay representing the incubation period of avian influenza is incorporated into our model to make it more realistic, which is different from the traditional Filippov model. The stability of various types of equilibria and the existence of Hopf bifurcation are researched. Moreover, the existence of the sliding mode and its dynamics are investigated by Filippov convexity method. The theoretical analysis and numerical simulations indicate that, according to the value of thresholds and time delay, all solutions eventually converge to the regular equilibrium, pseudoequilibrium or stable periodic solution. We also indicate that time delay has a great influence on the sliding mode. Due to the many factors involved, and our main purpose is to study the impact of time delay on system stability, we have only conducted a simple analysis of the impact of time delay on the sliding mode. Furthermore, the boundary bifurcation switching stable regular equilibrium or stable limit cycle to a stable pseudoequilibrium can be exhibited by numerical simulations. Finally, with the increase of time delay, the global bifurcations from grazing bifurcation to buckling bifurcation and then to cross bifurcation are obtained. Our results indicate that although Filippov control strategies can effectively control the number of infected birds in many cases, the existence of time delay may challenge influenza control by the emergence of buckling bifurcation and cross bifurcation.

Unexpected versatile electrical transport behaviors of ferromagnetic nickel films

Perpendicular magnetic anisotropy (PMA) of magnets is paramount for electrically controlled spintronics due to their intrinsic potentials for higher memory density, scalability, thermal stability and endurance, surpassing an in-plane magnetic anisotropy (IMA). Nickel film is a long-lived fundamental element ferromagnet, yet its electrical transport behavior associated with magnetism has not been comprehensively studied, hindering corresponding spintronic applications exploiting nickel-based compounds. Here, we systematically investigate the highly versatile magnetism and corresponding transport behavior of nickel films. As the thickness reduces within the general thickness regime of a magnet layer for a memory device, the hardness of nickel films’ ferromagnetic loop of anomalous Hall effect increases and then decreases, reflecting the magnetic transitions from IMA to PMA and back to IMA. Additionally, the square ferromagnetic loop changes from a hard to a soft one at rising temperatures, indicating a shift from PMA to IMA. Furthermore, we observe a butterfly magnetoresistance resulting from the anisotropic magnetoresistance effect, which evolves in conjunction with the thickness and temperature-dependent magnetic transformations as a complementary support. Our findings unveil the rich magnetic dynamics and most importantly settle down the most useful guiding information for current-driven spintronic applications based on nickel film: The hysteresis loop is squarest for the ∼8 nm-thick nickel film, of highest hardness with Rxy r /Rxy s ∼ 1 and minimum Hs −Hc , up to 125 K; otherwise, extra care should be taken for a different thickness or at a higher temperature.

BIFURCATION ANALYSIS OF AN SIR MODEL WITH SATURATED INCIDENCE RATE AND STRONG ALLEE EFFECT

In this paper, rich dynamics and complex bifurcations of an SIR epidemic model with saturated incidence rate and strong Allee effect are investigated. First, the existence of disease-free and endemic equilibria is explored, and we prove that the system has at most three positive equilibria, which exhibit different types such as hyperbolic saddle and node, degenerate unstable saddle (node) of codimension 2, degenerate saddle-node of codimension 3 at disease-free equilibria, and cusp, focus, and elliptic types Bogdanov–Takens singularities of codimension 3 at endemic equilibria. Second, bifurcation analysis at these equilibria are investigated, and it is found that the system undergoes a series of bifurcations, including transcritical, saddle node, Hopf, degenerate Hopf, homoclinic, cusp type Bogdanov–Takens of codimensional 2, and focus and elliptic type Bogdanov–Takens bifurcation of codimension 3 which are composed of some bifurcations with lower codimension. The system shows very rich dynamics such as the coexistence of multiple periodic orbits and homoclinic loops. Finally, numerical simulations are conducted on the theoretical results.

Confinement effect on the microcapillary flow and shape of red blood cells.

The ability to change shape is essential for the proper functioning of red blood cells (RBCs) within the microvasculature. The shape of RBCs significantly influences blood flow and has been employed in microfluidic lab-on-a-chip devices, serving as a diagnostic biomarker for specific pathologies and enabling the assessment of RBC deformability. While external flow conditions, such as the vessel size and the flow velocity, are known to impact microscale RBC flow, our comprehensive understanding of how their shape-adapting ability is influenced by channel confinement in biomedical applications remains incomplete. This study explores the impact of various rectangular and square channels, each with different confinement and aspect ratios, on the in vitro RBC flow behavior and characteristic shapes. We demonstrate that rectangular microchannels, with a height similar to the RBC diameter in combination with a confinement ratio exceeding 0.9, are required to generate distinctive well-defined croissant and slipper-like RBC shapes. These shapes are characterized by their equilibrium positions in the channel cross section, and we observe a strong elongation of both stable shapes in response to the shear rate across the different channels. Less confined channel configurations lead to the emergence of unstable other shape types that display rich shape dynamics. Our work establishes an experimental framework to understand the influence of channel size on the single-cell flow behavior of RBCs, providing valuable insights for the design of biomicrofluidic single-cell analysis applications.

A Quad‐Unit Dielectric Elastomer Actuator for Programmable Two‐Dimensional Trajectories

Resonant actuation and multi‐degree‐of‐freedom (DoF) actuation can optimize the output matrices and greatly expand the versatility of dielectric elastomer actuators (DEAs) for practical applications. However, developing a multi‐DoF resonant DEA that benefits both from the maximized stroke outputs in resonant actuation and the versatility in multi‐DoF actuation remains a challenging task due to the slow responses of the widely adopted acrylic elastomers and the exponentially scaled complexity in the nonlinear dynamics. Herein, a multi‐DoF resonant DEA is reported by adopting four radially organized planar DE units fabricated by low‐loss silicone elastomers to output versatile programmable two‐dimensional quasi‐static and resonant trajectories. The rich nonlinear dynamics of the proposed quad‐unit DEA (QUDEA) are characterized and the critical parameters for two‐dimensional trajectory programming are uncovered through extensive modeling and experimental studies. To showcase the two‐dimensional trajectory programming capabilities of the QUDEA, demonstrations of Chinese characters writing and hummingbird flapping patterns mimicking using the proposed QUDEA are developed. The proposed QUDEA is expected to have potential in various applications such as in experimental biology, biomimetic robotics, and industrial manufacturing devices.

Coupled action potential and calcium dynamics underlie robust spontaneous firing in dopaminergic neurons

Dopaminergic neurons are specialized cells in the substantia nigra, tasked with dopamine secretion. This secretion relies on intracellular calcium signaling coupled to neuronal electrical activity. These neurons are known to display spontaneous calcium oscillations in-vitro and in-vivo, even in synaptic isolation, controlling the basal dopamine levels. Here we outline a kinetic model for the ion exchange across the neuronal plasma membrane. Crucially, we relax the assumption of constant, cytoplasmic sodium and potassium concentration. We show that sodium-potassium dynamics are strongly coupled to calcium dynamics and are essential for the robustness of spontaneous firing frequency. The model predicts several regimes of electrical activity, including tonic and ‘burst’ oscillations, and predicts the switch between those in response to perturbations. ‘Bursting’ correlates with increased calcium amplitudes, while maintaining constant average, allowing for a vast change in the calcium signal responsible for dopamine secretion. All the above traits provide the flexibility to create rich action potential dynamics that are crucial for cellular function.

Replicator-mutator dynamics of the rock-paper-scissors game: Learning through mistakes.

We generalize the Bush-Mosteller learning, the Roth-Erev learning, and the social learning to include mistakes, such that the nonlinear replicator-mutator equationwith either additive or multiplicative mutation is generated in an asymptotic limit. Subsequently, we exhaustively investigate the ubiquitous rock-paper-scissors game for some analytically tractable motifs of mutation pattern for which the replicator-mutator flow is seen to exhibit rich dynamics that include limit cycles and chaotic orbits. The main result of this paper is that in both symmetric and asymmetric game interactions, mistakes can sometimes help the players learn; in fact, mistakes can even control chaos to lead to rational Nash-equilibrium outcomes. Furthermore, we report a hitherto-unknown Hamiltonian structure of the replicator-mutator equation.

Neuromorphic auditory classification based on a single dynamical electrochemical memristor

Designing compact computing hardware and systems is highly desired for resource-restricted edge computing applications. Utilizing the rich dynamics in a physical device for computing is a unique approach in creating complex functionalities with miniaturized footprint. In this work, we developed a dynamical electrochemical memristor from a static memristor by replacing the gate material. The dynamical device possessed short-term fading dynamics and exhibited distinct frequency-dependent responses to varying input signals, enabling its use as a single device-based frequency classifier. Simulation showed that the device responses to different frequency components in a mixed-frequency signal were additive with nonlinear attenuation at higher frequency, providing a guideline in designing the system to process complex signals. We used a rate-coding scheme to convert real world auditory recordings into fixed amplitude spike trains to decouple amplitude-based information and frequency-based information and was able to demonstrate auditory classification of different animals. The work provides a new building block for temporal information processing.

Optimizing echo state networks for continuous gesture recognition in mobile devices: A comparative study

Continuous gesture recognition can be used to enhance human-computer interaction. This can be accomplished by capturing human movement with the use of the Inertial Measurement Units in smartphones and using machine learning algorithms to predict the intended gestures. Echo State Networks (ESNs) consist of a fixed internal reservoir that is able to generate rich and diverse nonlinear dynamics in response to input signals that capture temporal dependencies within the signal. This makes ESNs well-suited for time series prediction tasks, such as continuous gesture recognition. However, their application has not been rigorously explored, with regard to gesture recognition. In this study, we sought to enhance the efficacy of ESN models in continuous gesture recognition by exploring diverse model structures, fine-tuning hyperparameters, and experimenting with various training approaches. We used three different training schemes that used the Leave-one-out Cross-validation (LOOCV) protocol to investigate the performance in real-world scenarios with different levels of data availability: Leaving out data from one user to use for testing (F1-score: 0.89), leaving out a fraction of data from all users to use in testing (F1-score: 0.96), and training and testing using LOOCV on a single user (F1-score: 0.99). The obtained results outperformed the Long Short-Term Memory (LSTM) performance from past research (F1-score: 0.87) while maintaining a low training time of approximately 13 seconds compared to 63 seconds for the LSTM model. Additionally, we further explored the performance of the ESN models through behaviour space analysis using memory capacity, Kernel Rank, and Generalization Rank. Our results demonstrate that ESNs can be optimized to achieve high performance on gesture recognition in mobile devices on multiple levels of data availability. These findings highlight the practical ability of ESNs to enhance human-computer interaction.

Multistability, relaxation oscillations, and chaos in time-delayed optoelectronic oscillators with direct laser modulation.

We investigate the nonlinear dynamics of an optoelectronic oscillator that is implemented with a laser diode (LD) with time-delayed feedback. In this system, electrical-to-optical conversion is directly implemented using the direct modulation of the laser diode itself, instead of an electrooptical modulator as in conventional architectures. Moreover, we consider the cubic nonlinear saturation of the characteristic laser power-intensity (P-I) transfer function far above threshold, instead of its simplified piecewise linear counterpart. We perform the stability analysis of the oscillator, and we show that it displays a rich dynamics that includes quasi-harmonic, relaxation oscillations, and chaos. We also show that the oscillator is strongly hysteretic and displays a wide variety of multistable behaviors, including the rare case of bistability between chaotic attractors. Our analytical and numerical results are found to be in good agreement with the experimental measurements.

The role of natural recovery category in malaria dynamics under saturated treatment.

In the process of malaria transmission, natural recovery individuals are slightly infectious compared with infected individuals. Our concern is whether the infectivity of natural recovery category can be ignored in areas with limited medical resources, so as to reveal the epidemic pattern of malaria with simpler analysis. To achieve this, we incorporate saturated treatment into two-compartment and three-compartment models, and the infectivity of natural recovery category is only reflected in the latter. The non-spatial two-compartment model can admit backward bifurcation. Its spatial version does not possess rich dynamics. Besides, the non-spatial three-compartment model can undergo backward bifurcation, Hopf bifurcation and Bogdanov-Takens bifurcation. For spatial three-compartment model, due to the complexity of characteristic equation, we apply Shengjin's Distinguishing Means to realize stability analysis. Further, the model exhibits Turing instability, Hopf bifurcation and Turing-Hopf bifurcation. This makes the model may admit bistability or even tristability when its basic reproduction number less than one. Biologically, malaria may present a variety of epidemic trends, such as elimination or inhomogeneous distribution in space and periodic fluctuation in time of infectious populations. Notably, parameter regions are given to illustrate substitution effect of two-compartment model for three-compartment model in both scenarios without or with spatial movement. Finally, spatial three-compartment model is used to present malaria transmission in Burundi. The application of efficiency index enables us to determine the most effective method to control the number of cases in different scenarios.

Introduction to dynamical mean-field theory of randomly connected neural networks with bidirectionally correlated couplings

Dynamical mean-field theory is a powerful physics tool used to analyze the typical behavior of neural networks, where neurons can be recurrently connected, or multiple layers of neurons can be stacked. However, it is not easy for beginners to access the essence of this tool and the underlying physics. Here, we give a pedagogical introduction of this method in a particular example of random neural networks, where neurons are randomly and fully connected by correlated synapses and therefore the network exhibits rich emergent collective dynamics. We also review related past and recent important works applying this tool. In addition, a physically transparent and alternative method, namely the dynamical cavity method, is also introduced to derive exactly the same results. The numerical implementation of solving the integro-differential mean-field equations is also detailed, with an illustration of exploring the fluctuation dissipation theorem.

Shaping photons: Quantum information processing with bosonic cQED

With its rich dynamics, the quantum harmonic oscillator is an innate platform for understanding real-world quantum systems and could even excel as the heart of a quantum computer. A particularly promising and rapidly advancing platform that harnesses quantum harmonic oscillators for information processing is the bosonic circuit quantum electrodynamics (cQED) system. In this article, we provide perspectives on the progress, challenges, and future directions in building a bosonic cQED quantum computer. We describe the main hardware building blocks and how they facilitate quantum error correction, metrology, and simulation. We conclude with our views of the key challenges that lie on the horizon, as well as scientific and cultural strategies for overcoming them and building a practical quantum computer with bosonic cQED hardware.

Annihilation mechanisms for interacting skyrmions in magnetic nanowire

Abstract Magnetic skyrmions are considered potential candidates for spintronics-based memory and logic devices. For achieving high-density and high-speed devices, it is essential to study their interactions. In this paper, the interaction, dynamics, and annihilation mechanisms of Néel skyrmions in nanowire confinement under the influence of spin-transfer torque (STT) and edge forces have been studied. Initially isolated, two Néel skyrmions are brought into proximity, leading to distinct interaction scenarios characterized by varying current densities. We explore the impact of these interactions on skyrmion trajectories, size evolution, and annihilation phenomena. Our findings reveal the interplay of skyrmion-skyrmion repulsive forces, edge effects, and the influence of STT, shedding light on the rich dynamics of these topological magnetic textures. Furthermore, we unveil the distinct annihilation mechanisms of the leading and trailing skyrmions under different forces, providing valuable insights into the fundamental physics of skyrmion behavior in confined geometries.

Bifurcations and global dynamics of a predator–prey mite model of Leslie type

AbstractIn this paper, we study a predator–prey mite model of Leslie type with generalized Holling IV functional response. The model is shown to have very rich bifurcation dynamics, including subcritical and supercritical Hopf bifurcations, degenerate Hopf bifurcation, focus‐type and cusp‐type degenerate Bogdanov–Takens bifurcations of codimension 3, originating from a nilpotent focus or cusp of codimension 3 that acts as the organizing center for the bifurcation set. Coexistence of multiple steady states, multiple limit cycles, and homoclinic cycles is also found. Interestingly, the coexistence of two limit cycles is guaranteed by investigating generalized Hopf bifurcation and degenerate homoclinic bifurcation, and we also find that two generalized Hopf bifurcation points are connected by a saddle‐node bifurcation curve of limit cycles, which indicates the existence of global regime for two limit cycles. Our work extends some results in the literature.