Search Results (292)

To mitigate low-speed speed oscillations in permanent magnet synchronous motors (PMSMs) arising from the combined effects of rotor-position-related periodic disturbances and external perturbations, this paper develops a composite robust speed regulation scheme that integrates non-singular terminal sliding mode control (NTSMC) with angle-domain iterative learning control (ILC). First, a non-singular terminal sliding mode speed controller is established to remove the singularity inherent in conventional terminal sliding mode formulations while preserving finite-time error convergence. To further improve robustness and reduce chattering, an enhanced generalized super-twisting reaching law incorporating a continuous saturation function is introduced. Second, to compensate for periodic disturbances associated with rotor position, an angle-domain ILC law is constructed to iteratively learn the periodic speed-tracking error, thereby suppressing low-speed speed ripple. Meanwhile, an extended state observer (ESO) is incorporated to estimate aperiodic disturbances online, enabling coordinated rejection of disturbances with different temporal characteristics. Experimental results demonstrate that the proposed composite strategy effectively weakens the dominant harmonic components in speed fluctuation and enhances low-speed operational smoothness, confirming the effectiveness of the developed method. Full article

In this paper, we investigate the multi-scale dynamics of a singularly perturbed Rosenzweig–MacArthur model with a generalist predator and identify dynamical phenomena, including equilibrium bifurcations, supercritical or subcritical singular Hopf bifurcations, canard explosion bifurcations and homoclinic bifurcations. Specifically, the system exhibits a globally stable node, a headless canard cycle evolving into a homoclinic cycle, a headed canard cycle encompassing either a headless canard cycle or a homoclinic cycle, and so on. Notably, near the boundary equilibrium, these cycles exhibit a diminutive beard-shaped structure whenever it aligns with the transcritical non-normally hyperbolic point. The numerical simulations confirm the occurrence of a canard explosion, relaxation oscillation, and an inverse canard explosion phenomena not previously reported in singularly perturbed systems with both a transcritical point and a canard point. In brief, our results demonstrate that the generalist predation can cause richer bifurcations and dynamics. Full article

The on-chip detection of circularly polarized light is pivotal for advancing applications in quantum optics, information processing, and spectroscopic sensing. However, conventional chiral metasurfaces often suffer from complex multilayer fabrication, material incompatibility, or modest performance, hindering their integration with photonic circuits. Here, we introduce a monolithic all-silicon metasurface that overcomes these limitations through a singular structural innovation. By strategically truncating four corners of a conventional Z-shaped meta-atom, we induce a hybridization of optical modes that profoundly enhances chiral light–matter interaction. This deliberately engineered perturbation yields a colossal circular dichroism with an extinction ratio exceeding 66 dB, a performance that surpasses existing state-of-the-art designs by approximately three orders of magnitude. Furthermore, the proposed metasurface exhibits remarkable fabrication robustness, owing to its single-layer architecture and CMOS-compatible material. We demonstrate that this exceptional metasurface can be directly integrated with a Mercury Cadmium Telluride (MCT) photodetector to form a highly efficient, compact circular polarization detector. Our work provides a simple yet powerful paradigm for creating high-performance chiral photonic devices, paving the way for their widespread adoption in integrated optoelectronics. Full article

Noise contamination is a common challenge in the analysis of time series data, where stochastic perturbations can obscure deterministic dynamics and complicate the interpretation of signals from chaotic and physiological systems. Reliable identification of noise regimes and their intensity is therefore essential for robust analysis of dynamical and biomedical signals, where incorrect attribution of stochastic perturbations can lead to misleading interpretations of system behavior. For this reason, the present study examines the role of complexity-based descriptors for identifying stochastic perturbations in time series and analyzes how these metrics respond to different noise regimes across heterogeneous dynamical systems. A supervised learning approach based on complexity descriptors was developed to analyze controlled perturbations in multiple signal types. Gaussian, pink, and low-frequency noise disturbances were injected at predefined intensity levels into the Rössler and Lorenz chaotic systems, the Hénon map, and synthetic electrocardiogram signals, while AR(1) processes were used for validation on inherently stochastic signals. From these systems, eighteen entropy-based, fractal, statistical, and singular value decomposition-based complexity metrics were extracted from either raw signals or reconstructed phase spaces. These features were used to perform three classification tasks that capture different aspects of noise characterization, including detecting the presence of noise, identifying the perturbation type, and discriminating between different noise intensities. In addition to predictive modeling, the study evaluates the complexity profiles and feature relevance of the metrics under varying perturbation regimes. The results show that no single complexity metric consistently discriminates noise regimes across all systems. Instead, system-specific relevance patterns emerge. Under given experimental constraints (data partitioning, machine learning algorithm, etc.), Approximate Entropy provides the strongest discrimination for the Lorenz system and the Hénon map, the Coefficient of Variation, Sample and Permutation Entropy dominate classification for ECG signals, and the Condition Number and Variance of first derivative together with Fisher Information are most informative for the Rössler system. Across all datasets, the proposed framework achieves an average accuracy of 99% for noise presence detection, 98.4% for noise type classification, and 98.5% for noise intensity classification. These findings demonstrate that complexity metrics capture structural and statistical signatures of stochastic perturbations across a diverse set of dynamic systems. Full article

We study axial perturbations of Reissner–Nordström black holes within the general framework of parity-violating modified gravity theories. We derive the governing equations for a class of frame-dragging perturbations, focusing on the symmetry structure and radial dependence of the perturbed metric component, describing its behavior across three distinct regions: near the singularity ($r\to 0$), between the inner and outer Reissner–Nordström horizons ($r_{-}<r<r_{+}$), and in the asymptotic exterior regime ($r\to \infty$). Using a combination of analytical and numerical methods, we analyze the solutions for varying black hole charge-to-mass ratios ($Q/M$) and angular momentum parameters (l). Key findings include the suppression of perturbations by the electromagnetic field for higher $Q/M$; the emergence of radial resonance-like behavior for specific l values; and a high degree of symmetry for solutions in the extremal limit ($Q/M\sim 1$), attributed to the AdS₂$\times S^2$ near-horizon geometry. The WKB approximation is employed to study the high-l regime, revealing quantized radial resonance modes and singular behavior in the extremal limit. Additionally, we explore the role of boundary conditions and the possibility of a Chern–Simons field $\mathsf{\Theta }$ as the source of the parity violation, showing that consistency and the behavior of the perturbations under time reversal demand a constant field (and thus no actually observable Chern–Simons effects) at leading order. These results provide a basis for further analysis of the stability and dynamical properties of charged black holes in parity-violating theories, with potential experimental signatures in gravitational wave observations. Full article

A conceptually consistent understanding is sought for the interactions sampled by the imaginary cubic oscillator with potential $V^{\left(ICO\right)}\left(x\right)=\mathrm{i}{x}^3$, which is by itself not acceptable as a meaningful quantum model due to a combination of its non-Hermiticity, unboundedness, and most of all the Riesz-basis non-diagonalizability of the Hamiltonian, known as its intrinsic exceptional point (IEP) feature. For the purposes of a perturbation-theory-based simulation of the emergence of such a singular system, a simplified (though not too strictly related) toy-model Hamiltonian is proposed. It combines an $N-$point discretization of the real line of coordinates with an ad hoc interaction in a two-parametric N-by-N-matrix Hamiltonian $H=H^{\left(N\right)}(A,B)$. After such a simplification, one can still encounter a somewhat weaker form of non-diagonalizability at the conventional Kato’s exceptional-point (EP) limit of parameters $(A,B)\to (A^{\left(EP\right)},B^{\left(EP\right)})$. The IEP-non-diagonalizability phenomenon itself appears mimicked by the less enigmatic EP degeneracy of the discrete toy model, especially at large $N\gg 1$. What we gain is that, in contrast to the IEP case, the regularization of the simplified toy model in vicinity to the black conventional EP becomes feasible. Full article

This paper investigates the asynchronous non-fragile $H_{\infty }$ control problem for a class of Markovian jump singularly perturbed systems (MJSPSs) with time-varying delays. By applying a multi-layer structure method, a non-fragile controller with time delay is designed for the MJSPSs to adapt to disturbances caused by nonstationary quantization and DoS attacks. To model the asynchronous dynamics between the system and the controller mode, an independent Markov chain is employed to capture the asynchronous quantization and control behavior. By constructing mode-dependent Lyapunov–Krasovskii functions, sufficient conditions are derived to ensure stochastic finite-time exponential stability and $H_{\infty }$ performance under conditions of delay, singular disturbances, and quantization uncertainty. The effectiveness of the method is validated using an inverted pendulum system controlled by a DC motor, demonstrating its ability to achieve robust stability and performance in bandwidth-constrained network environments. Full article

The unimodular version of the Kaluza–Klein theory is briefly discussed, and its projection onto four-dimensional spacetime is constructed. Imposing the unimodularity condition on the five-dimensional Kaluza–Klein metric, det$g_{AB}=1$ is equivalent to introducing a cosmological term in Einstein’s equations in four dimensions with a scalar field of the Brans–Dicke type. Singularity-free cosmological solutions with scalar field and matter sources are constructed, and their basic properties are analyzed In the present paper, attention is focused on the perturbative analysis of cosmological solutions, providing insights into their stability against small fluctuations. Full article

We show that recent numerical findings of universal scaling relations in systems of noisy, aligning self-propelled particles by Rüdiger Kürstencan robustly be explained by perturbation theory and known results for the Mathieu equation with purely imaginary parameter. In particular, we highlight the significance of a cascade of exceptional points that leads to non-trivial fractional scaling exponents in the singular-perturbation limit of high activity. Crucially, these features are rooted in the Fokker–Planck operator corresponding to free self-propulsion. This can be viewed as a dynamical phase transition in the dynamics of noisy active matter. We also predict that these scaling relations depend on the symmetry of the alignment interactions and discuss the relevance of this structure in the free propagation for self-alignment and cohesion-type interactions. Full article

The present work is focused on a predator–prey model with the Holling type II interaction function, which is influenced by diffusion, advection and nonlinear reaction effects. Firstly, we show that the solutions of this dynamical model are bounded and unique. Secondly we use the Lyapunov function and then show that the equilibrium points are globally stable. Thirdly, we obtain the solution profile when the diffusion coefficient is small. For this purpose we introduce self-similar structures to convert the nonlinear partial differential equations into nonlinear ordinary differential equations and then use the singular perturbation technique to solve these equations. Fourthly, we use the Hamiltonian and Lighthill’s technique to obtain upper stationary solutions for a small coefficient of the advection term. Lastly, we consider a large diffusion coefficient and obtain the asymptotic profiles of nonstationary solutions with the help of nonlinear point scaling. Full article

Phase transition in quantum mechanics is interpreted as an evolution, at the end of which, typically, a parameter-dependent and Hermitizable Hamiltonian $H\left(g\right)$ loses its observability. In the language of mathematics, such a “quantum catastrophe” occurs at an exceptional point of order N (EPN). Although the Hamiltonian $H\left(g\right)$ itself becomes unphysical in the limit of $g\to g^{EPN}$, it is shown that it can play the role of an unperturbed operator in an innovative perturbation-approximation analysis of the vicinity of the EPN singularity. As long as such an analysis is elementary at $N\le 3$ and purely numerical at $N\ge 5$, we pick up $N=4$ and demonstrate that for an arbitrary quantum system, the specific (i.e., already sufficiently phenomenologically rich) EP4 degeneracy becomes accessible via a unitary evolution process. This process is shown realizable inside a parametric domain ${\mathcal{D}}_{\mathrm{physical}}$, the boundaries of which are determined, near $g^{EP4}$, non-numerically. Possible relevance of such a mathematical result in the context of non-Hermitian photonics is emphasized. Full article

We examine the effects from small, spatially localized permanent charges on ionic transport in narrow membrane channels. Our analysis is based on a one-dimensional steady-state Poisson–Nernst–Planck (PNP) model involving two oppositely charged ion species with constant diffusion coefficients under electroneutral boundary conditions. In the framework of geometric singular perturbation theory, the steady PNP system is reformulated as a fast–slow dynamical system amenable to boundary-layer analysis. In the limit of vanishing permanent charge, the solution exhibits a singular structure with sharp boundary-layer segments and smooth bulk segments across regions of piecewise constant charge. Assuming the permanent charge strength Q is small, we carry out a regular perturbation expansion about $Q=0$ and derive explicit first-order corrections to each ion’s flux. Closed-form expressions are obtained for both the leading-order (zero-charge) fluxes and the $O\left(Q\right)$ flux corrections, revealing how even a small fixed charge can modulate the magnitude of individual ionic fluxes as a function of the applied transmembrane voltage and boundary concentration asymmetry. These results elucidate how permanent charge enhances or inhibits specific ionic flows, thereby influencing channel selectivity. Overall, our analysis provides clear asymptotic formulas and highlights the broader relevance of this perturbative approach to electro-diffusive transport modeling in biophysical systems. Full article

This paper introduces a distributed sensitivity-conditioning approach for bilevel optimization in networked microgrids. The proposed method enhances the coordination between subsystems by embedding sensitivity-based predictive terms into the dynamic updates, thereby improving convergence stability without requiring strict time-scale separation. Unlike conventional singular perturbation techniques, the sensitivity-conditioning formulation enables faster and more robust convergence of the distributed dynamics under heterogeneous subsystem speeds. The approach is applied to a networked microgrid scenario where local agents perform decentralized optimization considering both internal generation and energy exchange with neighboring microgrids. Simulation results demonstrate that the proposed algorithm achieves efficient coordination, reduces convergence time, and maintains stability under diverse operating conditions. The results highlight the method’s potential as a scalable and computationally efficient alternative for real-time distributed energy management and bilevel control in power network applications. Full article

The neutron survival probability (and related quantities including probabilities of extinction and initiation) is a central element of the broader stochastic theory of neutron populations and finds application in fields including reactor start-up, analysis of reactor power bursts and criticality accidents, and safeguards. In a full neutron transport formulation, the equation governing the single-neutron survival probability is a backward or adjoint-like integro-partial differential equation with the added complexity of being highly nonlinear. Analogous formulations of this equation exist in the context of many approximate theories of neutron transport, with the point kinetics formulation having received significant theoretical attention since the 1940s. This work continues this tradition by providing a novel analysis of the single-neutron survival probability equation using the tools of boundary layer theory. The analysis reveals that the “fully dynamic” solution of the single-neutron survival probability equation—and some key probability distributions derived from it—may be cast as a singular perturbation around the underlying quasi-static single-neutron probability of initiation. In this perturbation solution, the expansion parameter is the ratio of the neutron generation time to a macroscopic time scale characterizing the overall system evolution; this interpretation illuminates some of the fundamental structural aspects of neutron survival phenomena. Full article

Free gases of spinless fermions moving on a lattice-symmetric geometric background are considered. Their topological properties at zero temperature can be used to classify their Fermi seas and associated boundaries. The flat orbifolds ${\mathbb{R}}^d/\mathrm{\Gamma }$, where $\mathrm{\Gamma }$ is the crystallographic group of symmetry in d-dimensional momentum space, are used to accomplish this task. Two topological classes exist for $d=1$: an interval, which is identified as a conductor, and a circumference, which corresponds to an insulator. The number of topological classes increases to 17 for $d=2$: 8 have the topology of a disk, that are generally recognized as conductors, and 4 correspond to a two-sphere, matching insulators. Both sets eventually contain a finite number of conical singularities and reflection corners at the boundaries. The remaining cases in the listing relate to conductors (annulus, Möbius strip) and insulators (two-torus, real projective plane, Klein bottle). Examples that fall under this list are given, along with physical interpretations of the singularities. It is anticipated that the findings of this classification will be robust under perturbative interactions due to its topological character. Full article