Nonlinear Dynamics Research Articles

Harnessing collisional nonlinearity for enhanced harmonic generation by ultraviolet plasmonic nanoparticles.

We investigate the contribution of inelastic electron collisions to nonlinear (NL) dynamics in ultraviolet plasmonic nanoparticles, exploring their potential for harmonic generation. Employing the Landau weak coupling formalism to model radiation-driven electron dynamics in sodium and aluminum, we account for both electron-electron and electron-phonon scattering processes by a set of hydrodynamic equations, which we solve perturbatively to obtain third-order NL susceptibilities. Furthermore, we model high harmonic generation enhanced by localized surface plasmons in nanospheres composed of such poor metals, demonstrating their efficient operation for extreme ultraviolet generation. Our investigation reveals that plasmonic nanospheres composed of sodium and aluminum produce a large field intensity enhancement of ≃103-105, boosting the harmonic generation process. Our findings indicate that poor metals hold great promise for advanced extreme ultraviolet nano-sources with potential applications in nano-spectroscopy.

Semi-active control implementation in aircraft landing gear systems using hardware-in-the-loop test bench

In small-sized aircraft landing gear systems, magnetorheological (MR) dampers offer an innovative approach to adjusting damping levels under wide range of operating situations in order to achieve competing control objectives such as ride comfort, suspension travel, and energy consumption. Also, MR dampers have nonlinear dynamics and exhibit hysteresis. In this context, this paper aims to present a Hardware-In-the-Loop (HIL) technique for the implementation of backstepping control and linear quadratic regulator (LQR) control. Experimental results highlight that, compared to passive suspension (Passive Off), backstepping control and LQR control approaches reduce the fuselage vertical acceleration by 29.13% and 24.95%, respectively. Moreover, the ISO 2631 standard was adopted to evaluate ride comfort. LQR control can able to minimize the fuselage roll acceleration under a random road profile. Also, LQR control provides the highest performance in terms of fuselage roll acceleration, achieving a 6.2% improvement with lower energy consumption. By utilizing HIL, semi-active control methods can be tested and developed without the need for the aircraft, while keeping the characteristics that the physical aircraft would bring.

Command filtering‐based adaptive backstepping control for a class of discrete‐time uncertain nonlinear systems with mismatched disturbances

SummaryThis paper investigates the adaptive fuzzy backstepping control problem for uncertain discrete‐time nonlinear systems with mismatched disturbances. A novel adaptive fuzzy command filtered backstepping approach is proposed, which can overcome the noncausal problem by using the command filter. The filter errors generated by filter are removed by constructing error compensation mechanism. The fuzzy logic systems are used to approximate the uncertain nonlinear dynamics, and the unknown mismatched disturbances are actively attenuated by using adaptive control technique. Based on the proposed new weighed Lyapunov functions, all the signals in the close‐loop system are proved to be uniformly ultimately bounded. The viability of proposed method is demonstrated by simulation results.

1D -FNO - Residual convolutional neural network autoregressive prediction model for deep water wave train evolution based on high-order spectral (HOS) data

Accurate prediction of deep-water wave dynamics is essential for ocean engineering, meteorology, and maritime safety. Traditional physical models, though effective, face significant computational and time challenges with complex nonlinear dynamics. This study introduces an autoregressive prediction model using a one-dimensional adaptive Fourier Neural Operator-Residual Convolutional Neural Network (1D-FNO-ResNet) to enhance prediction accuracy. We developed a high-precision single-step prediction model capable of capturing wave characteristics such as height and fluid particle velocity. A fine-tuning training strategy based on multi-step prediction errors was proposed for autoregressive evolution. Performance comparisons between the ResNet and FNO-ResNet models were made under various fine-tuning steps. A correction model was also introduced to control error accumulation, improving autoregressive prediction steps. The model's generalization performance was validated with modulated and random wave trains under different conditions, optimizing predictive stability and accuracy. This approach demonstrates efficient 1D deep-water wave evolution prediction, offering a novel deep learning solution for wave dynamics prediction in ocean engineering, supporting wave energy conversion device design and optimization.

SRS-Net: a universal framework for solving stimulated Raman scattering in nonlinear fiber-optic systems by physics-informed deep learning

As a crucial nonlinear phenomenon, stimulated Raman scattering (SRS) plays multifaceted roles involved in forward and inverse problems. In fibre-optic systems, these roles range from detrimental interference that impairs optical performance to beneficial effects that enables various devices such as Raman amplifier. To obtain solutions of SRS, various numerical methods customized for different scenarios have been proposed. However, these methods are time-consuming, low-efficiency, and experience-orientated, particularly in combined scenarios consisting of both forward and inverse problems. Inspired by physics-informed neural networks, we propose SRS-Net, which combines the efficient automatic differentiation and powerful representation ability of neural networks with the regularization of SRS physical laws, to obtain universal solutions for SRS of forward, inverse, and combined problems. We showcase the intuitive solving procedure and high-speed performance of SRS-Net through extensive simulations covering different scenarios. Additionally, we validate its capabilities in experiments involving the high-fidelity modelling of a wavelength division multiplexing system spanning the C + L-band with approximately 10 THz. The versatility of the SRS-Net framework extends beyond SRS, indicating its potential as a promising universal solution in other engineering problems with nonlinear dynamics governed by partial differential equations.

Nonlinear dynamics of energy harvesting system for cantilevered fluid-conveying pipes with stopper

Nonlinear dynamics of energy harvesting system for cantilevered fluid-conveying pipes with stopper

Assessing the Asymmetric Effect of Global Climate Anomalies on Food Prices: Evidence from Local Prices

AbstractThis paper uses time-varying smooth transition autoregressive model to investigate the asymmetric nature of El Niño Southern Oscillation (ENSO) —an exogenous climatic factor—with respect to the nonlinear dynamics of food prices in sub-Saharan Africa. Curating food price series from more than 1100 markets from 36 SSA countries, the study finds that ENSO (linearly or nonlinearly) affects roughly half of food prices considered, with most nonlinear models exhibiting strong asymmetric properties with shock-inflicted persistence. Moreover, in terms of the location of the burden of ENSO impact, I find a geographical and food product divide. Specifically, ENSO appears to be more efficacious on maize prices in Southern, Eastern, and some parts of Central Africa. Conversely, local rice, cassava, millet, and animal products are least affected. The policy implication of this dichotomy is that response to ENSO news should be subregion-specific rather than region-specific, depending on how the subregions absorb the shock.

A local and hierarchical Koopman spectral analysis of fluid dynamics

AbstractA local and hierarchical Koopman spectral analysis is proposed to extend Koopman spectral analysis typically used in a linear system or an ergodic process to its application in general nonlinear dynamics. The continuous and analytic Koopman eigenfunctions and eigenvalues, derived from operator perturbation theory, are capable of dealing with a nonlinear transition process with mathematical rigorousness. A proliferation rule is identified to derive high‐order eigenvalues and eigenfunctions from lower‐order ones, thus various spectral patterns may be generated through recursive proliferations. The locally linear map around each state constructs base local Koopman eigenvalues and eigenfunctions from an algebraic eigenvalue problem, and high‐order ones are generated via the proliferation rule to express the systematic nonlinearity. The aforementioned hierarchy simplifies the Koopman spectral analysis and is verified by studying the development of Kármán vortex streets. The triangular chain and the lattice distribution of Koopman eigenvalues confirm the critical role of the proliferation rule and the hierarchy structure of Koopman eigenvalues. The local spectral analysis on the transition process shows that the periodic flow forms as the growth rates of the critical Koopman modes reduce to zero, and meanwhile, the Koopman modes at the same frequency superpose on each other to form the well‐known Fourier or Floquet modes, where the latter are the enhanced nonlinear motions due to the alignment of Koopman eigenvalues with the critical ones.

Epistemic stability and nonlinear dynamics in selection of suboptimal cluster counts in medical images validation dataset as a cluster homogeneity measure

Epistemic stability and nonlinear dynamics in selection of suboptimal cluster counts in medical images validation dataset as a cluster homogeneity measure

Zakharov–Kuznetsov Equation for Describing Low-Frequency Nonlinear Dust Acoustic Perturbations in Saturn’s Dusty Magnetosphere

A description is given of low-frequency nonlinear dust acoustic waves in Saturn’s dusty magnetosphere, which contains electrons of two types (hot and cold) obeying the kappa distribution, magnetospheric ions, and charged dust particles. For the corresponding conditions, the derivation of the Zakharov–Kuznetsov equation is given, which describes the nonlinear dynamics of dust acoustic waves in the case of low frequencies and a pancake-shaped wave packet along an external magnetic field. It is shown that under the conditions of Saturn’s magnetosphere there exist solutions of the Zakharov–Kuznetsov equation in the form of one-dimensional and three-dimensional solitons. Possible observations of the considered solitons in future space missions are discussed.

Unveiling the nonlinear dynamics and optical soliton patterns of stochastic Manakov model in the presence of multiplicative white noise

Unveiling the nonlinear dynamics and optical soliton patterns of stochastic Manakov model in the presence of multiplicative white noise

Nonlinear dynamics in a public good game

Nonlinear dynamics in a public good game

Growth, poverty trap and escape

The well-known Solow growth model is the workhorse model of the theory of economic growth, which studies capital accumulation in a model economy as a function of time with capital stock, labour and technology-based production as the basic ingredients. The capital is assumed to be in the form of manufacturing equipment and materials. Two important parameters of the model are: the saving fraction s of the output of a production function and the technology efficiency parameter A , appearing in the production function. The saved fraction of the output is fully invested in the generation of new capital and the rest is consumed. The capital stock also depreciates as a function of time due to the wearing out of old capital and the increase in the size of the labour population. We propose a stochastic Solow growth model assuming the saving fraction to be a sigmoidal function of the per capita capital kp . We derive analytically the steady state probability distribution P(kp) and demonstrate the existence of a poverty trap, of central concern in development economics. In a parameter regime, P(kp) is bimodal with the twin peaks corresponding to states of poverty and well-being, respectively. The associated potential landscape has two valleys with fluctuation-driven transitions between them. The mean exit times from the valleys are computed and one finds that the escape from a poverty trap is more favourable at higher values of A. We identify a critical value of Ac below (above) which the state of poverty (well-being) dominates and propose two early signatures of the regime shift occurring at Ac . The economic model, with conceptual foundations in nonlinear dynamics and statistical mechanics, shares universal features with dynamical models from diverse disciplines like ecology and cell biology.

How viscous bubbles collapse: Topological and symmetry-breaking instabilities in curvature-driven hydrodynamics

The duality between deformations of elastic bodies and noninertial flows in viscous liquids has been a guiding principle in decades of research. However, this duality is broken when a spheroidal or other doubly curved liquid film is suddenly forced out of mechanical equilibrium, as occurs, e.g., when the pressure inside a liquid bubble drops rapidly due to rupture or controlled evacuation. In such cases, the film may evolve through a noninertial yet geometrically nonlinear surface dynamics, which has remained largely unexplored. We reveal the driver of such dynamics as temporal variations in the curvature of the evolving surface. Focusing on the prototypical example of a floating bubble that undergoes rapid depressurization, we show that the bubble surface evolves via a topological instability and a subsequent front propagation, whereby a small planar zone that includes a singular flow structure, analogous to a disclination in elastic systems, nucleates spontaneously and expands in the spherically shaped film. This flow pattern brings about hoop compression and triggers another, symmetry-breaking instability to the formation of radial wrinkles that invade the flattening film. Our analysis reveals the dynamics as a nonequilibrium branch of "jellium" physics, whereby a rate-of-change of surface curvature in a viscous film is akin to charge in an electrostatic medium that comprises polarizable and conducting domains. We explain key features underlying recent experiments and highlight a qualitative inconsistency between the prediction of linear stability analysis and the observed "wavelength" of surface wrinkles.

Nonlinearity in affect dynamics persists after accounting for the valence of daily-life events.

In recent years, increased attention has gone to studying nonlinear characteristics of affective time series. An example of such nonlinear features is multimodality-the presence of more than one mode in an affective time series-which might mark the presence of discrete-like transitions between one and another affective state. In an attempt to capture these nonlinear features, Loossens et al. (2020) proposed the Affective Ising Model (AIM) as a model of affect dynamics. This model was validated on daily-life data, but these data did not contain any information on potential environmental factors that might have influenced a participant's affective state. Unfortunately, this omission may have led to erroneously concluding that nonlinearity is a defining characteristic of the affective system, even when it is solely driven by extrinsic influences. To accommodate this limitation, we applied the AIM on daily-life data in which the valence of such external events was measured. Overall, we found that nonlinearity persisted after accounting for the valence of daily-life events, suggesting that nonlinearity is a defining characteristic of affect and should thus be accounted for. Interestingly, this effect was more pronounced for composite compared to single-item measures of affect. While in line with previous research, these results should be replicated in a larger, more representative sample. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Neural Network-Based Fixed-Time Tracking and Containment Control of Second-Order Heterogeneous Nonlinear Multiagent Systems.

This study concentrates on the fixed-time tracking consensus and containment control of second-order heterogeneous nonlinear multiagent systems (MASs) with and without measurable velocity under directed topology. By defining a time-varying scaling function and approximating the unknown nonlinear dynamics with radial basis function neural networks (RBFNNs), a novel distributed protocol for solving the fixed-time tracking consensus and containment control problems of second-order heterogeneous nonlinear MASs with full states available is proposed based on a nonsingular sliding-mode control method constructed by designing a prescribed-time convergent sliding surface. For the scenario of immeasurable velocity, a fixed-time convergent states' observer is designed to reveal the velocity information when the unknown linearity is bounded. Subsequently, a distributed fixed-time consensus protocol based on observed velocity information is proposed for the extended results. Ultimately, the acquired results are verified by three simulation examples.

Nonlinear Dynamics and Meshing State Transition Analysis of Spalling Defect Gears with Multi-Lubrication Conditions

The purpose of this paper is to analyze the dynamic characteristics and the meshing state transition characteristics of spalling defect gears under various lubrication conditions. The time-varying geometric parameters, motion parameters and load distribution of the gears in the state of positive meshing and reverse impact are analyzed. The time-varying meshing stiffness considering the time-varying friction coefficient under elastohydrodynamic lubrication (EHL), mixed lubrication and boundary lubrication are calculated, and the spalling defect is introduced in the stiffness calculation process. The equivalent lubrication model of the gear is established, the switching condition of the lubrication state is derived, and the distribution of the lubrication state in the torque-speed plane is discussed. The multimeshing state dynamic model of the spalling defect gear is established, and the evolution characteristics of the coexistence response and the transition of the meshing state under different lubrication conditions are simulated by using the attraction domain, phase trajectory, meshing force and bifurcation diagram. The results show that the phase trajectory of the gear with the spalling defect is deformed compared with that of the healthy gear. The change of lubrication state has little effect on the phase trajectory and attraction domain of the gear with spalling defect, but has a great influence on the meshing force. At the spalling boundary, the meshing force is changed abruptly, and the worse the lubrication state, the more obvious the mutation. Due to the influence of spalling on tooth stiffness, it will also affect the meshing force in the nonspalling area.

Fuzzy Fault Detection Observer Design for Unmanned Marine Vehicles Based on Membership-Function-Dependent H∞/H_ Performance

This paper studies the design problem of fault detection (FD) observer for unmanned marine vehicles (UMVs) based on the T-S fuzzy model. Firstly, T-S fuzzy systems are used to approximate the nonlinear dynamics in UMVs. Secondly, to improve the FD performance of UMVs, a new H∞/H_ performance index, which depends on the membership functions, is defined. Then, based on the membership-function-dependent H∞/H_ performance index, a new fuzzy FD observer strategy, where the fuzzy submodels are not all required to be with the same H_ performance index, is developed to detect the sensor fault in UMVs; the corresponding synthesis conditions of the FD observer are derived based on the Lyapunov theory. Different from the conventional FD strategies, in the proposed membership-function-dependent FD method, the fuzzy submodels—which the system always works on—can have a larger H_ performance index, such that the performance of the FD can be improved. In the end, an example is given to show the effectiveness of the presented method.

Advancing Offshore Renewable Energy: Integrative Approaches in Floating Offshore Wind Turbine-Oscillating Water Column Systems Using Artificial Intelligence-Driven Regressive Modeling and Proportional-Integral-Derivative Control

This research investigates the integration of Floating Offshore Wind Turbines (FOWTs) with Oscillating Water Columns (OWCs) to enhance sustainable energy generation, focusing on addressing dynamic complexities and uncertainties inherent in such systems. The novelty of this study lies in its dual approach, which integrates regressive modeling with an aero-hydro-elasto-servo-mooring coupled system with a deep data-driven network and implements a proportional-integral-derivative (PID) control mechanism to improve system stability. By employing Artificial Neural Networks (ANNs), the study circumvents the challenges of real-time closed-loop control on FOWT structures using the OpenFAST simulation tool. Data-driven models, trained on OpenFAST datasets, facilitate real-time predictive behavior analysis and decision-making. Advanced computational learning techniques, particularly ANNs, accurately replicate the dynamics of FOWT-OWC numerical models. An intelligent PID control mechanism is subsequently applied to mitigate structural vibrations, ensuring effective control. A comparative analysis with traditional barge-based FOWT systems underscores the enhanced modeling and control methodologies’ effectiveness. In this sense, the experimental results demonstrate substantial reductions in the mean oscillation amplitude, with reductions from 5% to 35% observed across various scenarios. Specifically, at a wave period from 20 s and a wind speed of 5 m/s, the fore-aft displacement was reduced by 35%, exemplifying the PID control system’s robustness and efficacy under diverse conditions. This study highlights the potential of ANN-driven modeling as an alternative to managing the complex non-linear dynamics of NREL 5 MW FOWT models and underscores the significant improvements in system stability through tailored PID gain scheduling across various operational scenarios.

Probabilistic Estimation and Control of Dynamical Systems Using Particle Filter with Adaptive Backward Sampling

Estimating and controlling dynamical systems from observable time-series data are essential for understanding and manipulating nonlinear dynamics. This paper proposes a probabilistic framework for simultaneously estimating and controlling nonlinear dynamics under noisy observation conditions. Our proposed method utilizes the particle filter not only as a state estimator and a prior estimator for the dynamics but also as a controller. This approach allows us to handle the nonlinearity of the dynamics and uncertainty of the latent state. We apply two distinct dynamics to verify the effectiveness of our proposed framework: a chaotic system defined by the Lorenz equation and a nonlinear neuronal system defined by the Morris–Lecar neuron model. The results indicate that our proposed framework can simultaneously estimate and control complex nonlinear dynamical systems.