Chaos最新文献

We investigate the entrainment of electrochemical oscillators with different phase response curves (PRCs) using a global signal: the goal is to achieve the desired phase configuration using a minimum-power waveform. Establishing the desired phase relationships in a highly nonlinear networked system exhibiting significant heterogeneities, such as different conditions or parameters for the oscillators, presents a considerable challenge because different units respond differently to the common global entraining signal. In this work, we apply an optimal phase-selective entrainment technique in both a kinetic model and experiments involving electrochemical oscillators in achieving phase synchronized states. We estimate the PRCs of the oscillators at different circuit potentials and external resistance, and entrain pairs and small sets of four oscillators in various phase configurations. We show that for small PRC variations, phase assignment can be achieved using an averaged PRC in the control design. However, when the PRCs are sufficiently different, individual PRCs are needed to entrain the system with the expected phase relationships. The results show that oscillator assemblies with heterogeneous PRCs can be effectively entrained to desired phase configurations in practical settings. These findings open new avenues to applications in biological and engineered oscillator systems where synchronization patterns are essential for system performance.

In this work, we investigate how the seasonal variation in the number of individuals who are tested for an HIV antibody in outpatient clinics affects the HIV transmission patterns in China, which has not been well studied. Based on the characteristics of outpatient testing data and reported cases, we establish a periodic infectious disease model to study the impact of seasonal testing on HIV transmission. The results indicate that the seasonal testing is a driving factor for the seasonality of new cases. We demonstrate the feasibility of ending the HIV/AIDS epidemic. We find that the diagnostic rates related to testing play a crucial role in controlling the size of the epidemic. Specifically, when considering minimizing both infected individuals and diagnostic rates, the level of attention paid to undiagnosed infected individuals is always positively correlated with the optimal diagnostic rates, while the optimal diagnostic rates are negatively correlated with the size of the epidemic at the terminal time.

Transformations are a key tool in the qualitative study of dynamical systems: transformations to a normal form, for example, underpin the study of instabilities and bifurcations. In this work, we test, and when possible establish, an equivalence between two different artificial neural networks by attempting to construct a data-driven transformation between them, using diffusion maps with a Mahalanobis-like metric. If the construction succeeds, the two networks can be thought of as belonging to the same equivalence class. We first discuss transformation functions between only the outputs of the two networks; we then also consider transformations that take into account outputs (activations) of a number of internal neurons from each network. Whitney's theorem dictates the number of (generic) measurements from one of the networks required to reconstruct each and every feature of the second network. The construction of the transformation function relies on a consistent, intrinsic representation of the network input space. We illustrate our algorithm by matching neural network pairs trained to learn (a) observations of scalar functions, (b) observations of two-dimensional vector fields, and (c) representations of images of a moving three-dimensional object (a rotating horse). We also demonstrate reconstruction of a network's input (and output) from minimal partial observations of intermediate neuron activations. The construction of equivalences across different network instantiations clearly relates to transfer learning and will also be valuable in establishing equivalence between different machine learning-based tools.

We explore adaptive link change strategies that can lead a system to network configurations that yield ordered dynamical states. We propose two adaptive strategies based on feedback from the global synchronization error. In the first strategy, the connectivity matrix changes if the instantaneous synchronization error is larger than a prescribed threshold. In the second strategy, the probability of a link changing at any instant of time is proportional to the magnitude of the instantaneous synchronization error. We demonstrate that both these strategies are capable of guiding networks to chaos suppression within a prescribed tolerance, in two prototypical systems of coupled chaotic maps. So, the adaptation works effectively as an efficient search in the vast space of connectivities for a configuration that serves to yield a targeted pattern. The mean synchronization error shows the presence of a sharply defined transition to very low values after a critical coupling strength, in all cases. For the first strategy, the total time during which a network undergoes link adaptation also exhibits a distinct transition to a small value under increasing coupling strength. Analogously, for the second strategy, the mean fraction of links that change in the network over time, after transience, drops to nearly zero, after a critical coupling strength, implying that the network reaches a static link configuration that yields the desired dynamics. These ideas can then potentially help us to devise control methods for extended interactive systems, as well as suggest natural mechanisms capable of regularizing complex networks.

The synchronous meshing of the gear pair and the screw pair is a typical feature of the planetary roller screw mechanism. In order to fully derive and analyze the nonlinear dynamic characteristics of the system, this paper creatively incorporates the time-varying meshing stiffness of gear pair and the comprehensive transmission error into the research content. Combined with the thread contact force and friction force between the roller and the screw and between the roller and the nut, the nonlinear dynamic model of the planetary roller screw mechanism considering the meshing excitation of the gear pair is established. According to the time domain diagram, frequency domain diagram, phase plane diagram, Poincaré section diagram, three-dimensional spectrum diagram, and spatial phase diagram, the nonlinear behavior of the system is described in detail, and the bifurcation evolution process of the system under the excitation frequency parameters of the external load is revealed. In addition, based on the theory of multi-scale method and considering the variables such as meshing stiffness, meshing damping, and load fluctuation, the stability equation of the primary resonance of the system is derived. The analysis of the stability of the system under different working conditions shows that the parameters are selected within a reasonable range, which effectively reduces the primary common amplitude value and enhances the overall stability of the system. The research content improves the previous system dynamics modeling method and provides a theoretical basis for the nonlinear dynamics modeling method and parameter optimization design of the planetary roller screw mechanism.

Higher-order interactions exist widely in mobile populations and are extremely important in spreading epidemics, such as influenza. However, research on high-order interaction modeling of mobile crowds and the propagation dynamics above is still insufficient. Therefore, this study attempts to model and simulate higher-order interactions among mobile populations and explore their impact on epidemic transmission. This study simulated the spread of the epidemic in a spatial high-order network based on agent-based model modeling. It explored its propagation dynamics and the impact of spatial characteristics on it. Meanwhile, we construct state-specific rate equations based on the uniform mixing assumption for further analysis. We found that hysteresis loops are an inherent feature of high-order networks in this space under specific scenarios. The evolution curve roughly presents three different states with the initial value change, showing different levels of the endemic balance of low, medium, and high, respectively. Similarly, network snapshots and parameter diagrams also indicate these three types of equilibrium states. Populations in space naturally form components of different sizes and isolations, and higher initial seeds generate higher-order interactions in this spatial network, leading to higher infection densities. This phenomenon emphasizes the impact of high-order interactions and high-order infection rates in propagation. In addition, crowd density and movement speed act as protective and inhibitory factors for epidemic transmission, respectively, and depending on the degree of movement weaken or enhance the effect of hysteresis loops.

Spin chains are correlated quantum models of great interest in quantum systems and materials exhibiting quasi-one-dimensional magnetic properties. Here, we review results on quantum problems associated with spin chains that are beyond the usual spinon paradigm. Alternatively, we use a representation valid in the thermodynamic limit, N→∞, in terms of the N spin-1/2 physical spins of the spin-1/2XXZ chain in its whole Hilbert space. It was originally introduced for the isotropic point in Carmelo et al. [Phys. Rev. B 92, 165133 (2015)], co-authored by David, and more recently extended to spin anisotropies Δ>1 in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)]. The physical-spins representation accounts for the spin-1/2XXZ chain's continuous SUq(2) symmetry parameterized by q=Δ+Δ2-1∈]1,∞] and associated with q-spin Sq. Specifically, in this review we consider two quantum problems that are beyond the spinon representation: (a) Spin Bethe strings of length n that have no spinon representation, contribute to the dynamical properties of the spin-1/2XXZ chain with anisotropy Δ>1 and for n=1,2,3 were experimentally identified and realized in the zigzag materials SrCo2V2O8 and BaCo2V2O8; (b) The spin stiffness associated with ballistic spin transport at arbitrary finite temperature, which involves a huge number of energy eigenstates, many of which are generated in the thermodynamic limit from ground states by an infinite number of elementary processes. As found in Carmelo et al. [Phys. Rev. Res. 5, 043058 (2023)] and J. M. P. Carmelo and P. D. Sacramento [Nucl. Phys. B 974, 115610 (2022); Nucl. Phys. B 997, 116385 (2023) (Corrigendum)], the use of the continuous SUq(2) symmetry reveals that for anisotropy Δ>1 the Bethe strings of length n=1,2,3,… describe a number n of physical-spins Sq=0 singlet pairs that for n>1 are bound within a Sq=0 singlet configuration. Their contribution to the spin dynamical structure factor of both the spin-1/2XXZ chain in a longitudinal magnetic field and the spin chains in SrCo2V2O8 is one of the issues addressed in this paper. In addition, the SUq(2) symmetry imposes that only 2Sq out of the N physical spins are the spin carriers. We also review recent results of J. M. P. Carmelo and P. D. Sacramento ["Diffusive spin transport of the spin-1/2 XXZ chain in the Ising regime at zero magnetic field and finite temperature," (submitted) (2024)] concerning the vanishing of the contributions to finite-temperature ballistic spin transport at zero magnetic field. Within the physical-spins representation, this merely follows from the absolute value of the elementary spin currents carried by the M=2Sq spin carriers of all finite-Sq states that contribute to the spin stiffness being finite. Finally, we discuss deviations of the zigzag materials BaCo2V2O8 and SrCo2V2O8 from the one-dimensional physics describe

Reservoir computing (RC) is a machine learning paradigm that excels at dynamical systems analysis. Photonic RCs, which perform implicit computation through optical interactions, have attracted increasing attention due to their potential for low latency predictions. However, most existing photonic RCs rely on a nonlinear physical cavity to implement system memory, limiting control over the memory structure and requiring long warm-up times to eliminate transients. In this work, we resolve these issues by demonstrating a photonic next-generation reservoir computer (NG-RC) using a fiber optic platform. Our photonic NG-RC eliminates the need for a cavity by generating feature vectors directly from nonlinear combinations of the input data with varying delays. Our approach uses Rayleigh backscattering to produce output feature vectors by an unconventional nonlinearity resulting from coherent, interferometric mixing followed by a quadratic readout. Performing linear optimization on these feature vectors, our photonic NG-RC demonstrates state-of-the-art performance for the observer (cross-prediction) task applied to the Rössler, Lorenz, and Kuramoto-Sivashinsky systems. In contrast to digital NG-RC implementations, we show that it is possible to scale to high-dimensional systems while maintaining low latency and low power consumption.

There has been strong interest recently in the so-called Cooper pair density wave, subsequent to the proposition that such a state occurs in the hole-doped cuprate superconductors. As of now, there is no convincing demonstration of such a state in the cuprate theoretical literature. We present here a brief but complete review of our theoretical and computational work on the paired-electron crystal (PEC), which has also been experimentally seen in the insulating phase proximate to superconductivity (SC) in organic charge-transfer solid (CTS) superconductors. Within our theory, SC in the CTS does indeed evolve from the PEC. A crucial requirement for the finding of the PEC is that the proper carrier density of one charge carrier per two sites is taken into consideration at the outset. Following the discussion of CTS superconductors, we briefly discuss how the theory can be extended to understand the phase diagram of the cuprate superconductors that has remained mysterious after nearly four decades of the discovery of SC in this family.

Electromagnetic radiation (EMR) affects the dynamical behavior of the nervous system, and appropriate EMR helps to study the dynamic mechanism of the nervous system. This paper uses a sophisticated four-dimensional Hopfield neural network (HNN) model augmented with one or more memristors to simulate the effects of EMR. We focus on the chaotic dynamics of HNN under the influence of EMR. Complex dynamical behaviors are found and transient chaotic phenomena have the same initial value sensitivity, showing how transient chaos is affected by EMR. Multiperiodic phenomena induced by quasi-periodic alternations are found in the dual EMR, as well as the suppression properties of the dual EMR for system chaos. This implies that the dynamical behavior of the HNN system can be controlled by varying the amount of EMR or the number of affected neurons in the HNN. Finally, a strong validation of our proposed model is provided by Multisim and Field Programmable Gate Array(FPGA) hardware.