Showing papers in "Nonlinear Dynamics in 2023"

An SEQAIHR model to study COVID-19 transmission and optimal control strategies in Hong Kong, 2022

Abstract: During the COVID-19 pandemic, one of the major concerns was a medical emergency in human society. Therefore it was necessary to control or restrict the disease spreading among populations in any fruitful way at that time. To frame out a proper policy for controlling COVID-19 spreading with limited medical facilities, here we propose an SEQAIHR model having saturated treatment. We check biological feasibility of model solutions and compute the basic reproduction number ( $$R_0$$ ). Moreover, the model exhibits transcritical, backward bifurcation and forward bifurcation with hysteresis with respect to different parameters under some restrictions. Further to validate the model, we fit it with real COVID-19 infected data of Hong Kong from 19th December, 2021 to 3rd April, 2022 and estimate model parameters. Applying sensitivity analysis, we find out the most sensitive parameters that have an effect on $$R_0$$ . We estimate $$R_0$$ using actual initial growth data of COVID-19 and calculate effective reproduction number for same period. Finally, an optimal control problem has been proposed considering effective vaccination and saturated treatment for hospitalized class to decrease density of the infected class and to minimize implemented cost.

Modeling and analysis of a piezoelectric transducer embedded in a nonlinear damped dynamical system

Abstract: Abstract This paper focuses on the dynamical analysis of the motion of a new three-degree-of-freedom (DOF) system consisting of two segments that are attached together. External harmonic forces energize this system. The equations of motion (EOM) are derived utilizing Lagrangian equations, and the approximate solutions up to the third order are investigated using the methodology of multiple scales. A comparison between these solutions and numerical ones is constructed to confirm the validity of the analytic solutions. The modulation equations (ME) are acquired from the investigation of the resonance cases and the solvability conditions. The bifurcation diagrams and spectrums of Lyapunov exponent are presented to reveal the different types of the system’s motion and to represent Poincaré maps. The piezoelectric transducer is connected to the dynamical system to convert the vibrational motion into electricity; it is one of the energy harvesting devices which have various applications in our practical life like environmental and structural monitoring, medical remote sensing, military applications, and aerospace. The influences of excitation amplitude, natural frequency, coupling coefficient, damping coefficient, capacitance, and load resistance on the output voltage and power are performed graphically. The steady-state solutions and stability analysis are discussed through the resonance curves.

A new (n+1)-dimensional generalized Kadomtsev–Petviashvili equation: integrability characteristics and localized solutions

Abstract: Searching for higher-dimensional integrable models is one of the most significant and challenging issues in nonlinear mathematical physics. This paper aims to extend the classic lower-dimensional integrable models to arbitrary spatial dimension. We investigate the celebrated Kadomtsev–Petviashvili (KP) equation and propose its (n+1)-dimensional integrable extension. Based on the singularity manifold analysis and binary Bell polynomial method, it is found that the (n+1)-dimensional generalized KP equation has N-soliton solutions, and it also possesses the Painlevé property, Lax pair, Bäcklund transformation as well as infinite conservation laws, and thus the (n+1)-dimensional generalized KP equation is proven to be completely integrable. Moreover, various types of localized solutions can be constructed starting from the N-soliton solutions. The abundant interactions including overtaking solitons, head-on solitons, one-order lump, two-order lump, breather, breather-soliton mixed solutions are analyzed by some graphs.

Benchmarking sparse system identification with low-dimensional chaos

Abstract: Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system identification across scientific domains, but there remains a gap in the literature for large-scale methodological comparisons that are evaluated on a variety of dynamical systems. In this work, we systematically benchmark sparse regression variants by utilizing the dysts standardized database of chaotic systems introduced by Gilpin (in: Advances in neural information processing systems (NeurIPS), 2021. arXiv:2110.05266 ). In particular, we demonstrate how this open-source tool can be used to quantitatively compare different methods of system identification. To illustrate how this benchmark can be utilized, we perform a large comparison of four algorithms for solving the sparse identification of nonlinear dynamics (SINDy) optimization problem, finding strong performance of the original algorithm and a recent mixed-integer discrete algorithm. In all cases, we used ensembling to improve the noise robustness of SINDy and provide statistical comparisons. In addition, we show very compelling evidence that the weak SINDy formulation provides significant improvements over the traditional method, even on clean data. Lastly, we investigate how Pareto-optimal models generated from SINDy algorithms depend on the properties of the equations, finding that the performance shows no significant dependence on a set of dynamical properties that quantify the amount of chaos, scale separation, degree of nonlinearity, and the syntactic complexity.

Design and dynamic performance research of MR hydro-pneumatic spring based on multi-physics coupling model

Abstract: Aiming at the problem that the damping coefficient of the traditional hydro-pneumatic spring cannot be adjusted in real-time, the magnetorheological (MR) damping technology was introduced into the traditional hydro-pneumatic spring with single gas chamber. A new shear-valve mode MR hydro-pneumatic spring was proposed. And its dynamic performance was analyzed based on multi-physical coupling simulation and mechanical property test. Firstly, a structural scheme of MR hydro-pneumatic suspension was proposed to ensure the original height adjustment function based on the working principle of traditional hydro-pneumatic suspension with single gas chamber. Secondly, based on the design requirements, the parameter of MR hydro-pneumatic spring damping structure was designed by using MR damper design method. Thirdly, the multi-physical coupling dynamic performance of the MR hydro-pneumatic spring damping structure was analyzed based on the electromagnetic field analysis theory, flow field analysis theory and thermal field analysis theory. The analysis results showed that the designed MR hydro-pneumatic spring has reasonable magnetic circuit structure and excellent working performance. Then, the mechanical properties of MR hydro-pneumatic spring were tested. The results showed that the maximum damping force can reach 20 kN, and the dynamic adjustable multiple can reach 6.4 times. It has good controllability and meets the design requirements. Finally, a nonlinear model of MR hydro-pneumatic spring was established based on the elastic force calculation model of the gas and the Bouc–Wen model. The simulation results of the established model agree well with the experimental results, which can accurately describe the dynamic properties of the hydro-pneumatic spring. The proposed design and modeling method of the MR hydro-pneumatic spring can provide a theoretical basis for the related vibration damping devices.

Travelling wave solution for the Landau-Ginburg-Higgs model via the inverse scattering transformation method

Abstract: Abstract The Landau-Ginzburg-Higgs (LGH) equation explains the ocean engineering models, superconductivity and drift cyclotron waves in radially inhomogeneous plasma for coherent ion-cyclotron waves. In this paper, with a simple modification of the Ablowitz-Kaup-Newell-Segur (AKNS) formalism, the integrability of LGH equation is proved by deriving the Lax pair. Hence for that, the inverse scattering transformation (IST) is applied, and the travelling wave solutions are obtained and graphically represented in 2d and 3d profiles.

A nonlinear tunable piezoelectric resonant shunt using a bilinear component: theory and experiment

Abstract: In this article, we propose a new concept for tuning a resonant piezoelectric shunt absorber thanks to the use of a nonsmooth electronic component. It consists in adding a voltage source in the resonant shunt circuit, which is a bilinear function of the voltage across the piezoelectric patch. The main advantage is the ability to change the electrical resonance frequency with the bilinear component gain, enabling a tuning as well as a possible reduction in the required inductance value. Furthermore, because of the intrinsic nonlinear nature of the bilinear component, a multi-harmonic response is at hand, leading to a nonlinear coupling between the mechanical and electrical modes. Two particular tunings between the electrical and the mechanical resonance frequencies are tested. The first one is one-to-one, for which the electrical resonance is tuned close to the mechanical one. It is proved to be similar to a classical linear resonant shunt, with the additional tuning ability. The second case consists in tuning the electrical circuit at half the mechanical resonance, leading to a two-to-one (2:1) internal resonance. The obtained response is also found to be similar to a classical resonant shunt near the main resonance. In either case, the shunt performances are analytically and numerically studied, leading to optimal values of the design parameters as well as an estimation of the amplitude reduction provided by the shunt. Finally, experimental validation is proposed, targeting the damping of the twisting mode of a hydrofoil structure, in which the bilinear component is realized with a diode.