Behavior Of Nonlinear Systems Research Articles

Lie point symmetry infinitesimals, optimal system, power series solution, and modulational gain spectrum to the mathematical Noyes–Field model of nonlinear homogeneous oscillatory Belousov–Zhabotinsky reaction

Introduction:The chemical oscillators are identified as open system that demonstrate periodic changes in the concentration of some reaction species as a result of intricate physico-chemical mechanisms which can lead to bi-stability, the occurrence of limit cycle attractors, the emergence of spiral waves and turing patterns, and finally, deterministic chaos. Objectives:The main objective of this paper is to analyze the simple Noyes–Field governing system of differential equations for the nonlinear Belousov–Zhabotinsky reaction which delineates the non-linear oscillatory behavior of chemical systems that occurs in the homogeneous media. Methodology:The Lie symmetry invariance analysis performed to extract the symmetries infinitesimal generators and the adjoint representation carried out to develop optimal system for the obtained Lie vectors. The significant power series approach applied to obtain the analytical solution. The modulation instability criteria ensured the stability of nonlinear oscillatory Belousov–Zhabotinsky reaction process. Results:The one-dimensional Lie symmetry generators algebra of the mathematical Noyes–Field governing system for oscillatory reaction is established. Furthermore, similarity reductions are carried out as well as the development of an optimal system of the sub-algebras. The similarity transformation technique converted the controlling system to ordinary differential equations and generates the large quantity of analytical traveling wave solutions. Moreover, the closed-form analytical solution for the proposed homogeneous nonlinear oscillatory chemical process is secured. The (MI) gain spectrum graphically visualized with the suitable choice of arbitrary parameters. Conclusion:The graphical performance of the Noyes–Field model solution at various settings reveals new perspectives and fascinating model phenomena. The attained outcomes have significant applications and have opened up innovative development areas for research across numerous scientific fields.

The Stochastic Ice-Sheet and Sea-Level System Model v1.0 (StISSM v1.0)

Abstract. We introduce the first version of the Stochastic Ice-sheet and Sea-level System Model (StISSM v1.0), which adds stochastic parameterizations within a state-of-the-art large-scale ice sheet model. In StISSM v1.0, stochastic parameterizations target climatic fields with internal variability, as well as glaciological processes exhibiting variability that cannot be resolved at the spatiotemporal resolution of ice sheet models: calving and subglacial hydrology. Because both climate and unresolved glaciological processes include internal variability, stochastic parameterizations allow StISSM v1.0 to account for the impacts of their high-frequency variability on ice dynamics and on the long-term evolution of modeled glaciers and ice sheets. StISSM v1.0 additionally includes statistical models to represent surface mass balance and oceanic forcing as autoregressive processes. Such models, once appropriately calibrated, allow users to sample irreducible uncertainty in climate prediction without the need for computationally expensive ensembles from climate models. When combined together, these novel features of StISSM v1.0 enable quantification of irreducible uncertainty in ice sheet model simulations and of ice sheet sensitivity to noisy forcings. We detail the implementation strategy of StISSM v1.0, evaluate its capabilities in idealized model experiments, demonstrate its applicability at the scale of a Greenland ice sheet simulation, and highlight priorities for future developments. Results from our test experiments demonstrate the complexity of ice sheet response to variability, such as asymmetric and/or non-zero mean responses to symmetric, zero-mean imposed variability. They also show differing levels of projection uncertainty for stochastic variability in different processes. These features are in line with results from stochastic experiments in climate and ocean models, as well as with the theoretical expected behavior of noise-forced non-linear systems.

Nonlinear Dynamic Analysis of Gas Bearing-Rotor System by the Hybrid Method Which Combines Finite Difference Method and Differential Transform Method

Gas bearings have been widely applied to high-speed rotating machines due to their low friction and high rotational speed advantages. Nevertheless, gas lubrication is low viscosity and compressible. It causes the gas bearing-rotor system easy to produce self-excited vibration, which leads to instability of the rotor system and hinders the increase of rotor system speed. It is necessary to study the nonlinear behaviors of the aerostatic bearing-rotor system and the nonlinear vibration of the gas bearing-rotor system, especially considering the distribution mass and flexible and gyroscopic effects of the real rotor. In this paper, the nonlinear behavior of the gas bearing-rotor system is investigated from the viewpoint of nonlinear dynamics. Firstly, the dynamics model of a gas bearing rotor is established by combining the transient Reynolds equation and rotor dynamic equation obtained by finite element method (FEM). The transient Reynolds equation is solved using a hybrid method combining the differential transform method (DTM) and finite difference method (FDM). Then the transient gas force is substituted into the FEM rotor dynamic equation. In the end, based on the bifurcation diagram, the orbit of the rotor center, the frequency spectrum diagram and Poincaré map, the rotor system’s nonlinear behaviors are studied using a solution for the rotor dynamic equation with the Newmark method. Results show that there exists a limited cycle motion in the autonomous rotor system and half-speed whirl in the nonautonomous rotor system.

Dynamic Process Safety Assessment Using Adaptive Bayesian Network with Loss Function

Fault detection and diagnosis (FDD) is crucial for dynamic process safety analysis. Integrated with failure prediction models, it enables us to realize how a deviation in process variable(s) can affect system safety (measured as risk). This work aims to overcome the challenges of nonlinear, non-Gaussian, and multimodal behavior of the processing systems to detect abnormal process operations, predict dynamic operational risk, and diagnose root cause of the abnormal situation. A methodology is proposed here by integrating different techniques. The artificial neural network (ANN) is used to identify process modes, while the Bayesian network (BN) is used for fault detection. How a fault will lead to a process failure is modeled using the event tree (ET), whereas time-dependent losses associated with the failure scenarios are assessed using the inverted normal loss function (INLF). A probability adaption mechanism is used to estimate the conditional probabilities in each time slice. The complexity of estimating conditional probabilities is handled using the copula theory. The proposed framework is validated using numerical, simulated, and industrial datasets. The results suggest that the developed framework can provide greater flexibility and wider applications.

Terahertz PHASR Scanner with 2 kHz, 100 picosecond Time-Domain Trace Acquisition Rate and an Extended Field-of-View Based on a Heliostat Design.

Recently, we introduced a Portable HAndheld Spectral Reflection (PHASR) Scanner to allow THz Time-Domain Spectroscopic (THz-TDS) imaging in clinical and industrial settings using a fiber-coupled and alignment-free telecentric beam steering design. The key limitations of the version 1.0 of the PHASR Scanner were its field-of-view and speed of time-domain trace acquisition. In this paper, we address these limitations by introducing a heliostat geometry for beam scanning to achieve an extended field-of-view, and by reconfiguring the Asynchronous OPtical Sampling (ASOPS) system to perform Electronically Controlled OPtical Sampling (ECOPS) measurements. The former change improved the deflection range of the beam, while also drastically reducing the coupling of the two scanning axes, the combination of which resulted in a larger than four-fold increase in the FOV area. The latter change significantly improves the acquisition speed and frequency domain performance simultaneously by improving measurement efficiency. To accomplish this, we characterized the non-linear time-axis sampling behavior of the electro-mechanical system in the ECOPS mode. We proposed methods to model and correct the non-linear time-axis distortions and tested the performance of the high-speed ECOPS trace acquisition. Therefore, here we introduce the PHASR Scanner version 2.0, which is capable of imaging a 40×27 mm2 FOV with 2000 traces per second over a 100 picosecond TDS range. This new scanner represents a significant leap towards translating the THz-TDS technology from the lab bench to the bedside for real-time clinical imaging applications.

A Remarkable Summation Formula, Lattice Tilings, and Fluctuations

We derive and prove an explicit formula for the sum of the fractional parts of certain geometric series. Although the proof is straightforward, we have been unable to locate any reference to this result. This summation formula allows us to efficiently analyze the average behavior of certain common nonlinear dynamical systems, such as the angle-doubling map, modulo 1. In particular, one can use this information to analyze how the behavior of individual orbits deviates from the global average (called fluctuations). More generally, the formula is valid in , where expanding maps give rise to so-called number systems. To illustrate the usefulness in this setting, we compute the fluctuations of a certain map on the plane.

Stable solitons and peakons, quantum information entropies, interactions, and excitations for generalized [formula omitted]-symmetric NLS equations

In this paper, a class of physically interesting PT-symmetric δ(x)-absolute-harmonic-Gaussian (PT-δ-AHG) potentials is explored in both linear and nonlinear wave regimes. In the linear regime, we find that the PT-δ-AHG potential can make the non-Hermitian Hamiltonian possess fully-real spectra for some parameter regions. In the nonlinear regime, we find the stable solitons, and single- and double-hump peakons for both focusing and defocusing generalized nonlinear Schrödinger (NLS) equations with PT-δ-AHG potentials. Moreover, the quantum information entropies of these nonlinear modes are investigated to explore the dynamic behaviors of PT nonlinear systems. Also, the dynamic interactions of exact solitons with incident solitary waves are discussed. Finally, we find that these bright solitons, single- and double-hump peakons can still stably propagate by means of adiabatic excitations, i.e., by slowly changing the parameters of the PT-δ-AHG potential, which implies that one can stably modulate the PT optical solitons. These interesting results will be helpful to further explore the relative PT nonlinear wave phenomena, and to design some physical experiments.

Nonlinear dynamic behavior of a dual-rotor bearing system with coupling misalignment and rubbing faults

Taking the dual-rotor system in an aero-engine as a research object, the vibration behaviors of a dual-rotor bearing system that is fault-free or has misalignment, rub-impact or misalignment rub-impact coupling faults are studied, respectively. First, the three-dimensional model of the dual rotor bearing system is established, and then the first six modes and critical speeds of the dual rotor bearing system are obtained by the finite element method. Then, the dynamic equations of the dual rotor bearing system with and without faults are derived based on the Lagrange method. The Runge–Kutta method is used to solve the dynamic equation, and the nonlinear dynamic response of the system is obtained. The vibrational behaviors of the dual rotor system with misalignment, rub-impact and misalignment rub-impact coupling faults are analyzed and discussed through the time history, phase diagram and frequency spectrum of the rotor. The vibrational behaviors of the first six modes of the dual rotor system with and without faults are analyzed, respectively. The results provide theoretical guidance for the structural optimization design of an aero-engine rotor system and the prior decision information for misalignment and rub-impact coupling fault diagnosis.

Nonlinear analysis and chaos synchronization of a memristive-based chaotic system using adaptive control technique in noisy environments

The behavior of memristor-based chaotic systems under the influence of external noise is the subject of recent work. In this paper, the nonlinear behavior of a new memristive chaotic system based on memcapacitor and meminductor is considered in noisy environments. The nonlinear behavior of the proposed memristive chaotic system in the presence of white Gaussian noise is viewed through a time series of dynamical analyses, Lyapunov exponent analysis, and phase diagram analysis. Then, chaos synchronization of two memristive chaotic systems in the presence of white gaussian noise is considered. For this purpose, adaptive feedback control laws are derived from achieving global chaos synchronization of identical new memristive chaotic systems. To confirm the validity of the proposed method, some numerical simulations follow identical synchronizations. Numerical simulations are performed to show the effectiveness of the proposed method.

Investigating the Fidelity of Explainable Artificial Intelligence Methods for Applications of Convolutional Neural Networks in Geoscience

Abstract Convolutional neural networks (CNNs) have recently attracted great attention in geoscience because of their ability to capture nonlinear system behavior and extract predictive spatiotemporal patterns. Given their black-box nature, however, and the importance of prediction explainability, methods of explainable artificial intelligence (XAI) are gaining popularity as a means to explain the CNN decision-making strategy. Here, we establish an intercomparison of some of the most popular XAI methods and investigate their fidelity in explaining CNN decisions for geoscientific applications. Our goal is to raise awareness of the theoretical limitations of these methods and to gain insight into the relative strengths and weaknesses to help guide best practices. The considered XAI methods are first applied to an idealized attribution benchmark, in which the ground truth of explanation of the network is known a priori, to help objectively assess their performance. Second, we apply XAI to a climate-related prediction setting, namely, to explain a CNN that is trained to predict the number of atmospheric rivers in daily snapshots of climate simulations. Our results highlight several important issues of XAI methods (e.g., gradient shattering, inability to distinguish the sign of attribution, and ignorance to zero input) that have previously been overlooked in our field and, if not considered cautiously, may lead to a distorted picture of the CNN decision-making strategy. We envision that our analysis will motivate further investigation into XAI fidelity and will help toward a cautious implementation of XAI in geoscience, which can lead to further exploitation of CNNs and deep learning for prediction problems.

Magnomechanically induced absorption and switching properties in a dispersively coupled magnon-qubit system

We theoretically study the non-linear behavior of a hybrid quantum magnomechanical system, where the system consisting of a superconducting qubit couples dispersively to a magnon–phonon mode. The magnetic excitations (magnons) can interact with the mechanical vibrations of the system via a magnomechanical interaction, which results in the formation of magnomechanically induced transparency in the output of the system. We investigate the system’s switching behavior in the dressed qubit anharmonicity of the system and shows the sharp bistable frequency switching of the magnon–excitons. The proposed model also shows a realistic scheme to measure the magnon-qubit dispersive shift in the absorption spectra of the probe field. The absorption spectrum induced by the dispersive coupling shows a series of asymmetric double Fano line shapes whose positions can be determined by the magnon-qubit driving field. Our results will provide a theoretical approach to understand the complex and dynamic non-linear interactions and may come up with great significance in the realization of quantum sensing applications of magnonic systems.

Research on Dynamic Characteristics of Rub-Impact of Progressive Cavity Pump with Rotation Speed

The dynamic characteristics of Progressive Cavity Pump (PCP) have an important influence on the stability of oil wells string system. A nonlinear dynamics model of rotor system was presented. The equations of unbalance rotor were established by the Lagrange approach and the vibration characteristics of the rotor system under rub-impact was analyzed by used the modern nonlinear dynamics and bifurcation theories, through numerical calculation. The bifurcation diagrams, time domain charts and Poincaré maps were obtained to analyze dynamic characteristics of the system and the results reveal the multiform complex nonlinear dynamic behavior of the rotor-bearing system under rub-impact. Moreover, the influence of the speed on the relatively stable speed of the rotor system was analyzed. These analysis results provide theoretical bases for the rotor system's status recognition, diagnosis as well as safe and economic operation.

Research on Dynamic Characteristics of Rub-Impact of Progressive Cavity Pump with Rotation Speed

The dynamic characteristics of Progressive Cavity Pump (PCP) have an important influence on the stability of oil wells string system. A nonlinear dynamics model of rotor system was presented. The equations of unbalance rotor were established by the Lagrange approach and the vibration characteristics of the rotor system under rub-impact was analyzed by used the modern nonlinear dynamics and bifurcation theories, through numerical calculation. The bifurcation diagrams, time domain charts and Poincaré maps were obtained to analyze dynamic characteristics of the system and the results reveal the multiform complex nonlinear dynamic behavior of the rotor-bearing system under rub-impact. Moreover, the influence of the speed on the relatively stable speed of the rotor system was analyzed. These analysis results provide theoretical bases for the rotor system's status recognition, diagnosis as well as safe and economic operation.

High-Performance Digital Multiloop Control of LLC Resonant Converters for EV Fast Charging With LUT-Based Feedforward and Adaptive Gain

The <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> resonant converter is typically adopted in battery charging applications due to its excellent performance in terms of efficiency, power density, and wide input/output voltage regulation. However, this converter is a complex high-order system characterized by a strong nonlinear behavior, featuring large variations of the small-signal gain/phase and pole location depending on the operating point. Consequently, these features pose substantial challenges in designing a closed-loop controller and providing constant dynamical performance over a wide operating range. Therefore, this article proposes a digital multiloop control strategy for <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> resonant converters ensuring constant closed-loop bandwidth and excellent disturbance rejection performance across the complete converter operating region. The control scheme consists of two cascaded voltage and current loops. To design and tune these controllers, a simplified <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> dual first-order small-signal model is proposed. The system nonlinear behavior affecting the current control loop is counteracted by a real-time controller gain adaptation process, which ensures constant control bandwidth. In particular, the adaptive gain values are provided by a static switching frequency lookup table obtained experimentally. Moreover, the steady-state switching frequency value is fed forward at the output of the current loop regulator, providing a further dynamical performance enhancement. The proposed control strategy and the controller design procedure are verified both in simulation and experimentally on a 15-kW <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">LLC</i> converter prototype. The results demonstrate the superior reference tracking and disturbance rejection performance of the proposed control strategy with respect to a state-of-the-art solution based on a proportional–integral regulator.

A multipoint prediction model for nonlinear displacement of concrete dam

AbstractMeasurement points are installed in concrete dams to monitor nonlinear displacement behavior of dam systems working in complex and aggressive environment. Most modeling works for predicting displacements of these measurement points are limited to single output in point‐by‐point modeling way, with little attention paid to partition‐based multipoint combined modeling. Therefore, a novel multipoint prediction model (MPM) for concrete dam displacement is proposed whose novelty lies in, first, a partition method for measurement points of dam engineering that considers waveform used to identify dam deformation trend and chaos used to describe overall stability and inherent stochasticity in nonlinear displacement series of dam system, and second, a multi‐output support vector machine optimized by an improved grey wolf optimizer with better hierarchy and information transmission. The monitoring data of a super‐high concrete arch dam are used to verify the proposed model. Results indicate that the MPM shows feasibility and generalization capability regarding dam engineering and reaches the performance level of single‐point benchmark models. Robustness, sensitivity, and reasonability of the model are also discussed by random noise, sliding window, and perturbations.

Diversity of optical soliton structures in the spinor Bose–Einstein condensate modeled by three-component Gross–Pitaevskii system

This paper pays attention to secure the different forms of optical soliton solutions to the spinor Bose–Einstein condensate. Three-component Gross–Pitaevskii (tc-GP) system which describes the F = 1 spinor Bose–Einstein condensate (BEC), with F denoting the atom’s spin, is used as a governing model to secure the solutions in BEC. Superfluidity and superconductivity are two properties of the low-temperature phenomenon that are associated with the BEC, which is formed by a diluted atomic gas. There has been an increasing interest in studying multi-component equations because they can be utilized to explain a wide range of complicated physical phenomena and have more dynamical structures of localized wave solutions. New extended direct algebraic method (NEDAM), a recently developed integration tool, is used to secure the solution. Different kinds of solitons, such as dark, singular, kink, bright–dark, complex and combined, are extracted. In addition, hyperbolic, exponential type and periodic solutions are guaranteed. Nonlinear partial differential equations (NLPDEs) are well-explained by the technique since it offers previously derived solutions and also extracts new exact solutions by incorporating the results of multiple procedures. In addition to discussing the physical representation of some solutions, we also plot 3D, 2D and contour graphs using the appropriate parameter values. The findings of this paper can improve the nonlinear dynamical behavior of a given system and demonstrate the efficacy of the methodology used. We believe that a large number of engineering model specialists will benefit from this research. Findings suggest that the algorithm employed is efficient, prompt, succinct and applicable to complex systems.

Construction of optical pulses and other solutions to optical fibers in absence of self-phase modulation

This paper investigates the optical solitons to the Biswas–Arshed equation (BAE) with third-order dispersion and self-steepening coefficients that communicate pulse propagation in fiber optics. The equation is considered where self-phase modulation is negligibly small and hence removed. Under different constraint conditions, the extended Fan sub-equation method (EFSEM) is used to derive the different kinds of solutions in the forms of bright, dark, singular, complex and combined solitons. In addition, Jacobi elliptic function (JEF) periodic, hyperbolic-type solutions are secured. This technique is useful for solving NLPDEs because it combines the results of numerous operations to provide previously extracted solutions as well as fresh solutions. While describing the physical representation of particular solutions, we also plot 3D, and 2D graphs by picking appropriate values for the solutions’ related parameters. On the basis of a comparison of our results with well-known ones, the study indicates that our answers are innovative. Nonlinear dynamical behavior of a particular system can be improved and the methodology applied can be shown to be effective by these findings. Engineering modelers will greatly benefit from this study, according to our opinion. Based on the results obtained, the computational method adopted is efficient and direct, as well as succinct and can be applied to complex systems.

Modal interactions of a dual-joint cylindrical shell system via Nonlinear Normal Modes

Bolted flange joints are commonly encountered in engineering structures. One specific challenge that is regularly encountered is the modeling of connecting interfaces between flanges. Indeed, for large amplitudes of vibration, due to discontinuity of the structure and mechanical contact of the connecting interface, clearances may occur between flanges and cause local stiffness loss, exhibiting complicated nonlinear dynamic behavior. In this paper, a simplified dynamic model for bolted flange joint via structural static analysis is proposed, in which the stiffness nonlinearity due to the non-smoothness of jointed interface is characterized by piecewise-smooth springs. The proposed simplified model has demonstrated good accuracy and precision in capturing the nonlinear dynamic characteristics of bolted flange connections. Following the simplified modeling technique and focusing on the stiffness nonlinearities, an analytical dual-joint system with free–free boundary conditions is established capturing the interaction of a longitudinal mode with two bending modes. The Harmonic Balance Method combined with Asymptotic Numerical Method (HBM–ANM) is utilized to estimate Nonlinear Normal Modes (NNMs) of the system, which provide an interpretation of the underlying nonlinear dynamic behavior, including bifurcation analysis, internal resonances characterization, and stability properties. Especially, internal resonances between the three modes can be triggered at high energy (oscillation amplitude) level, without having commensurate linear natural frequencies, leading to qualitative changes in periodic motions and internal loads environment of the system. The influences of linear frequency ratios and stiffness nonlinearity of each joint on the dynamics of the system are discussed in terms of NNMs. It is interesting to reveal that reducing the stiffness nonlinearity of joint may grow the complexity of the nonlinear dynamics of the system, from the perspective of motion stability, and trigger internal resonance with a complex topology. The studies in this paper provide an in-depth understanding of the nonlinear dynamic behavior of dual-joint systems, and the NNMs certainly represent a useful framework that could lead to a better dynamic design of jointed structures.

Impact of chloride channel on firing patterns of the fractional-order Morris–Lecar model

Fractional calculus as a new approach for modeling has been used widely to study the non-linear behavior of physical and biological systems with some degrees of fractionality or fractality using differential and integral operators with non integer-orders. In this paper, to explore different dynamical classes of the Morris–Lecar neuronal model with chloride channel, we extend its integer-order domain into a new fractional-order space using fractional calculus. The nonstandard finite difference (NSFD) method following the Grünwald–Letnikov discretization may be applied to discretize the model and obtain the fractional-order form. Fractional derivative order has been used as a new control parameter to extract variety of neuronal firing patterns that happen in real world application but the integer-order operator may not be able to reveal them. To find the impact of chloride channel on dynamical behaviors of this neuronal model, the phase portrait and time series analysis have been performed for different fractional-orders and input currents. Depending on different values for γ, the fractional-order Morris–Lecar model with a chloride channel reproduces quiescent, spiking and bursting activities the same as the fractional-order Morris–Lecar model without a chloride channel. We numerically discover the occurrence of hopf bifurcation, and homoclinic bifurcation for these two models. These results show that adding a chloride channel to this neuron does not affect the overall spiking patterns of the model, however, when we add this new ionic channel, the neuron needs higher input current as stimulus to fire action potential and spike.

On the study of optical soliton molecules of Manakov model and stability analysis

This paper studies the dynamical behavior of Manakov model which is modeled by two-component nonlinear Schrödinger equation (NLSE). This system models the propagation of soliton flow using group velocity dispersion (GVD) and self-steeping coefficients. By the assistance of two recently developed integration tools, namely, generalized exponential rational function method (GERFM) and new extended direct algebraic method (NEDAM), the different kinds of solutions in the forms of bright, dark, combo and complex solitons are extracted. These types of solutions are quite well-known as optical soliton molecules or pulses in the literature. Moreover, the hyperbolic, exponential and trigonometric function solutions are recovered. In addition, stability analysis of the system is also discussed. A comparison is made between our results and those that are well-known, and the study concludes that the solutions we’ve reached are novel. The significance of the results is illustrated by selecting appropriate parameter values for numerical simulation and physical explanations. For the nonlinear dynamical behavior of a given system, this paper’s results can improve it and demonstrate that the applied methodology is suitable. A wide range of experts in the field of engineering models will benefit from this research, according to our opinion.