Periodic Oscillations Research Articles

Stability and Bifurcation Exploration of Delayed Neural Networks With Radial-Ring Configuration and Bidirectional Coupling.

For decades, studying the dynamic performances of artificial neural networks (ANNs) is widely considered to be a good way to gain a deeper insight into actual neural networks. However, most models of ANNs are focused on a finite number of neurons and a single topology. These studies are inconsistent with actual neural networks composed of thousands of neurons and sophisticated topologies. There is still a discrepancy between theory and practice. In this article, not only a novel construction of a class of delayed neural networks with radial-ring configuration and bidirectional coupling is proposed, but also an effective analytical approach to dynamic performances of large-scale neural networks with a cluster of topologies is developed. First, Coates' flow diagram is applied to acquire the characteristic equation of the system, which contains multiple exponential terms. Second, by means of the idea of the holistic element, the sum of the neuron synapse transmission delays is regarded as the bifurcation argument to investigate the stability of the zero equilibrium point and the beingness of Hopf bifurcation. Finally, multiple sets of computerized simulations are utilized to confirm the conclusions. The simulation results expound that the increase in transmission delay may cause a leading impact on the generation of Hopf bifurcation. Meanwhile, the number and the self-feedback coefficient of neurons are also playing significant roles in the appearance of periodic oscillations.

A damping method of grid strapdown inertial navigation system for polar region

Abstract The conventional north-pointing inertial navigation system (INS) always points to the geographic north. However, when the system crosses the pole in the polar region, the geographic north quickly changes with 180 degrees, and the rate of change of the geographic north direction will be infinite. Secondly, when the latitude approaches to 90 degrees, which will lead to singularities in math for the angular velocity caused by vehicle motion. With its special definition and mechanization, the grid coordinate system can solve the above problems. Nevertheless, the error analysis of the grid strapdown INS shows that there are Schuler periodic and Foucault periodic oscillations, which badly degrade the accuracy of the strap-down INS. To address the problem, the external horizontal damping technology is adopted in this paper, wherein the external velocity is provided by the Doppler velocity log (DVL). Finally, the feasibility and the effectiveness of the external damping technology were verified by simulation.

Photo-induced non-collinear interlayer RKKY coupling in bulk Rashba semiconductors

The interplay between light-matter, spin-orbit, and magnetic interactions allows the investigation of light-induced magnetic phenomena that are otherwise absent without irradiation. We present our analysis of light-driven effects on the interlayer exchange coupling mediated by a bulk Rashba semiconductor in a magnetic multilayer. The collinear magnetic exchange coupling mediated by the photon-dressed spin-orbit coupled electrons of BiTeI develops light-induced oscillation periods and displays new decay power laws, both of which are enhanced with an increasing light-matter coupling. For magnetic layers with non-collinear magnetization, we find a non-collinear magnetic exchange coupling uniquely generated by light-driving of the multilayer. As the non-collinear magnetic exchange coupling mediated by the photon-dressed electrons of BiTeI is unique to the irradiated system and it is enhanced with increasing light-matter coupling, this effect offers a promising platform of investigation of light-driven effects on magnetic phenomena in spin-orbit coupled systems. In this platform, light properties, such as its intensity, can serve as external knobs for inducing non-collinear couplings of the interlayer exchange and for modulating the collinear couplings. Both of these effects signify the photo-generated modification in the spin textures of spin-orbit coupled electrons in BiTeI.

Application of the Point Defect Model to the Oscillatory Anodic Oxidation of Illuminated n-Type Silicon in the Presence of Fluoride Ions Using Electrochemical Impedance Spectroscopy

This work aims to provide insight into the oscillations occurring during the anodic electrooxidation of Si in fluoride-containing electrolytes using electrochemical impedance spectroscopy (EIS). The EIS measurements were conducted within less than a tenth of the oscillation periods allowing changes in the electrical properties of the silicon/oxide/electrolyte interfaces to be monitored during an oscillatory cycle. Application of the power law model to the experimental data revealed a significant change in resistivity at the oxide/semiconductor interface while the properties at the oxide/electrolyte interface remained constant and the oxide layer varied only by about 1 nm around an average value of about 4.9 nm. The application of the point defect model to the semiconductor/oxide/F−-containing electrolyte interface suggests that the oscillations are linked to the time delay between the production of oxygen vacancies at the Si/oxide interface and their consumption at the oxide/electrolyte interface.

Analysis of Dynamics of a Recurrent Infectious Disease SIRS Model with Age Structure and Two Delays

In this paper, an SIRS model with age structure is proposed for recurrent infectious diseases by incorporating infectious delay and temporary immunity delay. Analysis shows that the disease will eventually disappear when the basic reproduction number [Formula: see text]. No matter how the infection delay [Formula: see text] changes, as long as the temporary immunity loss delay [Formula: see text], the disease transmission will only be endemic and there will be no periodic oscillations when [Formula: see text]. Moreover, the stability and Hopf bifurcation will appear as [Formula: see text] increases from zero. It indicates that the duration of temporary immunity can affect the form of disease transmission within the population. Our numerical simulations verified the correctness of the theoretical results.

Periodic response and stability analysis of a bistable viscoelastic von Mises truss

This paper examines the effect of viscoelasticity on the periodic response of a lumped parameter viscoelastic von Mises truss. The viscoelastic system is described by a second-order equation that governs the mechanical motion coupled to a first-order equation that governs the time evolution of the viscoelastic forces. The viscoelastic force evolves at a much slower rate than the elastic oscillations in the system. This adds additional time scales and degrees of freedom to the system compared to its viscous counterparts. The focus of this study is on the system’s behavior under harmonic loading, which is expected to show both regular and chaotic dynamics for certain combinations of forcing frequency and amplitude. While the presence of chaos in this system has already been demonstrated, we shall concentrate only on the periodic solutions. The presence of the intrawell and interwell periodic oscillations is revealed using the Harmonic Balance method. The study also looks at the influence of parameter changes on the system’s behavior through bifurcation diagrams, which enable us to identify optimal system parameters for maximum energy dissipation. Lastly, we formulate an equivalent viscous system using an energy-based approach. We observe that a naive viscous model fails to capture the behavior accurately depending on the system and excitation parameters, as well as the type of excitation. This underscores the necessity to study the full-scale viscoelastic system.

Anomalous h/2e Periodicity and Majorana Zero Modes in Chiral Josephson Junctions.

Recent experiments reported that quantum Hall chiral edge state-mediated Josephson junctions (chiral Josephson junctions) could exhibit Fraunhofer oscillations with a periodicity of either h/e [Vignaud etal., Nature (London) 624, 545 (2023)NATUAS0028-083610.1038/s41586-023-06764-4] or h/2e [Amet etal., Science 352, 966 (2016)SCIEAS0036-807510.1126/science.aad6203]. While the h/e-periodic component of the supercurrent had been anticipated theoretically before, the emergence of the h/2e periodicity is still not fully understood. In this Letter, we systematically study the Fraunhofer oscillations of chiral Josephson junctions. In chiral Josephson junctions, the chiral edge states coupled to the superconductors become chiral Andreev edge states. We find that in short junctions, the coupling of the chiral Andreev edge states can trigger the h/2e-magnetic flux periodicity. Our theory resolves the important puzzle concerning the appearance of the h/2e periodicity in chiral Josephson junctions. Furthermore, we explain that when the chiral Andreev edge states couple, a pair of localized Majorana zero modes appear at the ends of the Josephson junction, which are robust and independent of the phase difference between the two superconductors. As the h/2e periodicity and the Majorana zero modes have the same physical origin in the wide junction limit, the Fraunhofer oscillation period could be useful in identifying the regime with Majorana zero modes.

A mechanism for slow rhythms in coordinated pancreatic islet activity

Insulin levels in the blood oscillate with a variety of periods, including rapid (5–10 min), ultradian (50–120 min), and circadian (24 h). Oscillations of insulin are beneficial for lowering blood glucose and disrupted rhythms are found in people with type 2 diabetes and their close relatives. These in vivo secretion dynamics imply that the oscillatory activity of individual islets of Langerhans are synchronized, although the mechanism for this is not known. One mechanism by which islets may synchronize is negative feedback of insulin on whole-body glucose levels. In previous work, we demonstrated that a negative feedback loop with a small time delay, to account for the time required for islets to be exposed to a new glucose concentration in vivo, results in small 3–6 islet populations synchronizing to produce fast closed-loop oscillations. However, these same islet populations could also produce slow closed-loop oscillations with periods longer than the natural islet oscillation periods. Here, we investigate the origin of the slow oscillations and the bistability with the fast oscillations using larger islet populations (20–50 islets). In contrast to what was observed earlier, larger islet populations mainly synchronize to longer-period oscillations that are approximately twice the delay time used in the feedback loop. A mean-field model was also used as a proxy for a large islet population to uncover the underlying mechanism for the slow rhythm. The heterogeneous intrinsic oscillation periods of the islets interferes with this rhythm mechanism when islet populations are small, and is similar to adding noise to the mean-field model. Thus, the effect of a time delay in the glucose feedback mechanism is similar to other examples of time-delayed systems in biology and may be a viable mechanism for ultradian oscillations.

Instability characteristics and heat transfer of a separator assisted dual-evaporators loop thermosyphon under heating power maldistribution condition

Thermosyphon loop with multiple evaporators has been widely used in the data centers thanks to its compact structure and local hot spot avoiding. However, under the heating power maldistribution condition, on account of the separation and convergence of flow steams from different evaporators, the instability of the system can be exacerbated which leads to premature failure and damage of servers. Thus, a separator assisted loop thermosyphon with dual evaporators had been proposed to improve its heat transfer performances and stability. An experimental study of the instability characteristics and heat transfer of the system are carried out under different filling ratios, cooling water temperatures and heating powers in this paper. To fully understand the interaction mechanism of two evaporators behind the oscillation, the visualization of flow patterns in the liquid tube and two-phase tube are observed as well. Results showed that during the oscillatory operation, since the evaporator2 (high heat load) circuit will circulate first, the variation of fluid temperature at evaporator1(low heat load) outlet lags others. Besides, when the inlet water temperature increases, the operating states of the system transfer from oscillatory operation to stable operation. When the filling ratio varies from 50 %-70 %, instability occurs in the system, the oscillation period increases from 115 s to 911 s and amplitude increases from 2.5 °C to 11.1 °C with an increase of the filling ratio. It should be noted that in our new system, it still can operate stably even when the heating power difference between two evaporators are as large as 350 W. In addition, alternatively oscillation in the two evaporators, maximum heat transfer coefficient of evaporator2 and minimum heat transfer coefficient of evaporator1 can be found when the heat load varies due to the mass competition between two circuits. According to above results, it is expected that the system could be beneficial to the application in the data center cooling.

Autonomous snap oscillator with only one steady state: dynamical probing, controls, pseudo-random number generation and difference synchronization

The theoretical probing, microcontroller implementation, amplitude controls, chaos control, -pseudo-random number generation (PRNG), and difference synchronization of autonomous snap oscillator with only one steady state (ASOOSS) are studied in this paper. The ASOOSS exhibits self-excited complex attractors, periodic oscillations, coexistence of chaotic hidden attractors with a stable steady state, and hidden chaotic attractors. The simulated attractors are endorsed by the microcontroller execution of ASOOSS. Then, the total and partial controls of the amplitude of ASOOSS are demonstrated by using newly inserted parameters. Moreover, the efficacy of the configured single controller in suppressing chaos within ASOOSS is demonstrated through both analytical and numerical analyses. Furthermore, the binary data generated by the ASOOSS-based PRNG successfully passes the NIST 800–22 statistical tests, providing proof of the random nature of the ASOOSS-based PRNG and making it suitable for digital applications based on chaos. Additionally, controllers are devised to enable differential synchronization of three identical coupled chaotic ASOOSS systems. The effectiveness of the differential synchronization approach is validated through numerical simulations of the coupled chaotic ASOOSS systems.

Josephson Diode Effect in Parallel-Coupled Double-Quantum Dots Connected to Unalike Majorana Nanowires.

We study theoretically the Josephson diode effect (JDE) when realized in a system composed of parallel-coupled double-quantum dots (DQDs) sandwiched between two semiconductor nanowires deposited on an s-wave superconductor surface. Due to the combined effects of proximity-induced superconductivity, strong Rashba spin-orbit interaction, and the Zeeman splitting inside the nanowires, a pair of Majorana bound states (MBSs) may possibly emerge at opposite ends of each nanowire. Different phase factors arising from the superconductor substrate can be generated in the coupling amplitudes between the DQDs and MBSs prepared at the left and right nanowires, and this will result in the Josephson current. We find that the critical Josephson currents in positive and negative directions are different from each other in amplitude within an oscillation period with respect to the magnetic flux penetrating through the system, a phenomenon known as the JDE. It arises from the quantum interference effect in this double-path device, and it can hardly occur in the system of one QD coupled to MBSs. Our results also show that the diode efficiency can reach up to 50%, but this depends on the overlap amplitude between the MBSs, as well as the energy levels of the DQDs adjustable by gate voltages. The present model is realizable within current nanofabrication technologies and may find practical use in the interdisciplinary field of Majorana and Josephson physics.

Penetration state recognition for tungsten inert gas welding via an alternating cusp-shaped magnetic field-assisted molten pool-oscillation

To ensure optimal penetration in direct current (DC) argon tungsten arc welding, a method was proposed to recognize the molten pool penetration during molten pool oscillation under alternating cusp-shaped magnetic field (ACSMF). An arc discharge model is established to analyze the oscillation mechanism of the molten pool under ACSMF. The periodic variation of arc shape induces the periodic oscillation to establish a mapping relationship with the fluctuation of arc voltage waveform. At the excitation current of 3 A and frequency of 10 Hz, the arc voltage waveform undergoes abrupt changes at 1.26 V and 1.37 V, corresponding to the critical and the full penetration states, respectively. The errors in identifying moving penetration are 0.8 % and 0.7 %, with a full penetration weld, demonstrating a penetration rate of 100 %, indicating effective penetration recognition. Arc sensing technology for tungsten inert gas (TIG) welding under ACSMF is poised for gradual application in single-side welding and double-side forming of medium and thick plates. It is anticipated to evolve towards real-time identification technology for molten pool penetration monitoring.

Revisiting the dead time effects of Insight-HXMT/ME on timing analysis

ABSTRACT Dead time is a common instrumental effect of X-ray detectors, which would alter the behaviour of timing properties of astronomical signals, such as distorting the shape of power density spectra (PDS), affecting the root-mean-square of potential quasi-periodic oscillation signals, etc. We revisit the effects of the dead time of Medium Energy X-ray telescope (ME) onboard Insight-HXMT based on the simulation of electronic read-out mechanism that causes the dead time and the real data. We investigate dead time effects on the pulse profile as well as the quasi–periodic oscillation (QPO) signals. The dead time coefficient suggests a linear correlation with the observed count rate in each phase bin of the pulse profile according to the simulation of periodic signal as well as the real data observed on Swift J0243.6+6124. The Fourier-amplitude-difference (FAD) method could well recover the intrinsic shape of the observed PDS in the case that the PDS is from two identical detectors. We apply this technique on ME, by splitting the nine FPGA modules into two groups. The results indicate that the FAD technique suits the case when two groups of detectors are not largely different; and the recovered PDS of Sco X-1 observed by ME slightly enhances the significance of the previously known QPO signal, meanwhile the root-mean-square of QPO is significantly improved. We provide the FAD correction tool implemented in HXMTDAS for users in the future to better analyse QPO signals.

Dynamical analysis and event-triggered adaptive finite-time prescribed performance control of the FO coupled MEMS resonators

This paper explores the dynamic behaviors and control method of weakly coupled micro-electro-mechanical system (MEMS) resonators with fractional-order (FO) dynamics. In the dynamics analysis session, Lyapunov exponents, bifurcation theory, and phase diagrams are used to analyze the effects of system parameters, coupling stiffness, and FO on the complex dynamical behaviors such as periodicity, pseudo-periodicity, and chaos oscillations. To suppress chaotic oscillations, a dynamic event-triggered finite-time prescribed performance controller is proposed. The unknown nonlinear functions are approximated through the interval type-3 fuzzy system (IT3FS) with an adaptive law. A novel finite-time prescribed performance function (finite-time PPF) is constructed to establish constrained boundaries for tracking errors. Compared with the existing PPFs, the proposed approach allows for more flexible setting of the convergence boundary before reaching steady-state. Subsequently, the constrained tracking errors are mapped to an unconstrained form using a nonlinear transformation function, whether the error constraint is symmetric or asymmetric. To circumvent the “explosion of complexity” arising from backstepping design process, a tracking differentiator (TD) is utilized. Additionally, to alleviate strain on communication resources, an event-triggered mechanism is devised to update control signals. The trigger threshold of the control signals can be adaptively adjusted based on the values of the Lyapunov function and the dynamic auxiliary variables. This control method guarantees finite-time convergence for all signals of the system. Finally, extensive simulations are performed to verify the effectiveness of the proposed algorithm.

A Hamiltonian for 1/1 rotational secondary resonances, and application to small satellites of Saturn and Jupiter

In this work, we study the dynamics of rotation of the small satellites Methone and Aegaeon and revisit previous works on the rotation of Prometheus, Metis, and Amalthea. In all cases, the surfaces of section computed with the standard spin–orbit model reveal that the synchronous regime with small amplitude of libration shares another large domain in the phase space. We reproduce and apply the hamiltonian theory given in Wisdom 2004 [1] to analytically characterize the detected structure as being a secondary resonance where the period of the physical libration is similar to the orbital period of the satellite. We also show that the amplitude of libration in the secondary resonance is always larger than in the case of the other mode. Since the current rotational states of these sorts of satellites should be synchronous, our results can be considered in evolutionary studies of their rotation.

Investigation into the DNA's conformations and their conversions from the phase transition theory

The functions and transformation mechanisms of nucleic acids in their various states are of great importance in physiology and pathology. Based on the Landau model, this study reveals the mechanism of the existence of chirality and the transformation rules between different chiral conformations by studying the Duffing oscillation response of the local gauge potential on the DNA chain. The research results show that normal chiral DNA and DNA configuration transition behaviors exhibit regular nonlinear periodic oscillations. Moreover, the gauge potential value approaches zero at the B-Z junction site, which may add a criterion for detecting Z-forming sites. In addition, external force and damping play a key role in the chiral gauge potential of nucleic acids, and they can influence, regulate and even control the configuration transition of nucleic acids. Finally, we verified the rationality of our theory by combining x-ray crystal diffraction data of multiple configurations of DNA. This study provides new insights into the behavior and function of chiral DNA in organisms, and provides new possibilities for regulating DNA conformational transition in the future.

Relationship between the SST diurnal cycle over the Tropical Western Pacific Ocean and subseasonal/seasonal oscillations: Associations with wind speed and outgoing longwave radiation

In this study, the relationship between SST diurnal cycle,10 m wind speed (W10) and Outgoing Longwave Radiation (OLR) is investigated. A wavelet spectral analysis was applied to SST hourly data to identify the SST diurnal cycle over the Tropical Western Pacific Ocean (TWPO). The SST diurnal cycle was identified as a prominent spectrum peak in waves with an oscillation period of 1 day. An inverse energy cascade hypothesis suggests that the energy from the SST diurnal cycle propagates and gets absorbed by waves within the subseasonal timescale. Three windows were selected to represent the diurnal (0–2 days), subseasonal (15–60 days), and seasonal (80–200 days) timescales. A wavelet-filtered analysis was performed in these windows, revealing inverse SST/ wind speed and direct SST/ OLR correlations over TWPO. These findings are consistent with empirical parametric models. Additionally, this study demonstrates the rectification mechanism of SST through a wavelet-filtered approach, identifying statistically significant correlations at the 5 % level within the diurnal window (0–2 days), particularly in the central tropical Pacific. Wavelet-filtered anomalies of SST, W10, and OLR along 50–160°E reveal the alternating dry and wet phase propagation across the Indo-Pacific in the subseasonal window, which is associated with the Madden-Julian Oscillation (MJO). Furthermore, westward propagating anomalies in the Indian Ocean and eastward propagating anomalies east of the Maritime Continent (MC) and within the Pacific were identified in the seasonal window, resembling patterns of Rossby and equatorial Kelvin waves, respectively.

Analysis of the dynamic behaviors of molten pool and keyhole for the oscillating laser welding of dissimilar materials stake welded T-joints with a gap

The dynamic behaviors of molten pool and keyhole have the significant effects on weld quality and joint performance. To investigate the circular shaped oscillating laser welding (OLW) of dissimilar materials stake welded T-joints with a gap between the face plate (FP) and web plate (WP), a dynamic model of molten pool and keyhole for the OLW of dissimilar materials stake welded T-joints with a gap is developed and the dynamic behaviors of molten pool and keyhole during the weld formation process are analyzed and discussed in detail. Based on the calculated results, it is found that the laser beam mainly radiates on the front wall of keyhole and the hump is formed on the rear wall of keyhole relative to the moving direction of laser beam at the FP welding stage. At the gap penetration stage, the keyhole opening at the molten pool bottom of FP shows the trumpet-shaped characteristic and the molten pool is divided into the upper and lower parts by the gap. The formed gas cavity is separated and fused with the keyhole several times at the WP welding stage. The gap around the gas cavity is disappeared after the reintegration of the upper and lower parts of molten pool. The depth of molten pool shows the periodic fluctuation characteristic with time and the fluctuation period is nearly the same as the oscillation period of laser beam during the OLW process.

A Complete Arduino-Based Mathematical Pendulum Experiment Tool with Real-Time Data Acquisition Using an Excel Spreadsheet

It is very important for students to understand the concept of simple harmonic motion, such as a mathematical pendulum. Students need an experiment tool on mathematical pendulums that is capable of providing measurement results of various physical quantities of mathematical pendulums accurately and precisely. This research aims to (1) describe the specifications of an Arduino-based mathematical pendulum experiment tool, (2) describe the results of measurements of acceleration due to gravity, and (3) describe the effect of changes in deviation on the period at small angles. This research used the experiment method. The research results showed that (1) the Arduino-based mathematical pendulum experiment device is equipped with an HC-SR04 ultrasonic sensor to measure the length of the string and an FC-51 infrared sensor to measure the period with a precision of 94.9% and accuracy of 99%, (2) the average result of acceleration due to gravity measurements at various string length was (9.72 ± 0.19) m/s<sup>2</sup>,and (3) the mathematical pendulum period between angles of 1-13 degrees did not show a significant difference, showing that at small angles, the oscillation period is not affected by deviation.

The dynamic analysis of the rumor spreading and behavior diffusion model with higher-order interactions

Rumor spreading occurs not only between two individuals but also among multiple individuals or influenced by groups. However, pairwise interactions in complex networks are insufficient to describe this process. In this study, we propose a rumor spreading model with higher-order interactions, in which the rumor propagation process is represented by simplicial complexes. By selecting the propagation coefficient and time delay as the threshold, the model shows richer dynamic behaviors, such as the bi-stability, discontinuous transition, forward bifurcation, backward bifurcation, Hopf bifurcation, and periodic oscillation. Besides, for exploring the collective behavior induced by rumors, the rumor synchronization model is first established by applying the adaptive feedback mechanism, which erects a theoretical bridge between rumor spreading and behavior diffusion. Moreover, an improved optimal control strategy considering system gains is performed to curb rumor diffusion. Numerical simulations suggest that rumor spreading models with higher-order interactions are more consistent with actual data than network-based ones. Our results may shed some light on comprehending higher-order interactions in rumor spreading and the coupling between rumor and behavior, and provide a promising approach to control rumors and irrational behaviors.