Time-periodic Systems Research Articles

Wave Speeds for a Time-Periodic Bistable Three-Species Lattice Competition System

In this paper, we consider propagation direction (which can be used to predict which species will occupy the habitat or win the competition eventually) of a bistable wave for a three-species time-periodic lattice competition system with bistable nonlinearity, aiming to address an open problem. As a first step, by transforming the competition system to a cooperative one, we study the asymptotic behavior for the bistable wave profile and then prove the uniqueness of the bistable wave speed. Secondly, we utilize comparison principle and build up two couples of upper and lower solutions to judge the sign of the bistable wave speed which partially provides the answer to the open problem. As an application, we reduce the time-periodic system to a space–time homogeneous system, we obtain the corresponding criteria and carry out numerical simulations to illustrate the availability of our results. Moreover, an interesting phenomenon we have found is that the two weak competitors can wipe out the strong competitor under some circumstances.

Existence of forced waves and gap formations for a Lotka-Volterra competition system with nonlocal dispersal in a time periodic shift habitat

This paper is devoted to the study of a class of time periodic Lotka-Volterra competition system with nonlocal dispersal and shifting habitats. By using some known results of the periodic KPP model and employing the iterative techniques, we prove that there exist two positive numbers $c_{0}(d_{1})$ and $c_{0}(d_{2})$ such that the system admits a forced wave provided that the forcing speed $c\in(-c_{0}(d_{2}),c_{0}(d_{1}))$. In addition, based on the theoretical results, we show that the gap formations exist for $c>c_{0}(d_{1})$ and $c<-c_{0}(d_{2})$.

Design, Devlopment and Evaluation of Gastroretentive Floating Microspheres of Glibenclamide: In-vitro In-vivo Studies .

The current research study was designed to characterize the ethyl cellulose act as a carrier mediator used to prepare a floating microsphere of glibenclamide for developed gastroretentive sustain release floating drug delivery. Different microspheres of glibenclamide were formulated by the emulsion solvent evaporation technique of glibenclamide with EC in different ratios by using two solvent systems (ethanol and chloroform). After evaluating the micropolitics properties, %of yield value, drug loading efficiency, entrapment efficiency, diameter and surface morphology of the microsphere by using DLS and SEM, in-vitro drug release in gastric content, in-vitro buoyancy, and in-vivo floatation using animal model, compatibility study by FTIR, DSC and any other analytical study to demonstrate all formulation (especially GM2) was showing excellent results. So this work shows great gastro etentive floating drug delivery system for prolonged periods of time which is very useful in future for further study.

Efficacy of exercise with the hybrid assistive limb lumbar type on physical function in mobility-limited older adults: A 5-week randomized controlled trial

BackgroundSarcopenia and frailty often worsen in older adults because of declines in activities of daily living and social connections that are associated with chronic diseases and traumatic injuries such as falls and fractures. Exercise intervention for sarcopenia can take >3 months to improve muscle mass, muscle strength, and walking speed. Thus, a specialized intervention system for shorter periods of time is needed. In this study, we aimed to evaluate the short-term efficacy of an exercise program using the wearable cyborg Hybrid Assistive Limb (HAL) lumbar type in physical function in mobility-limited older adults who do not require transition to long-term care. MethodsThis randomized, single-blind, parallel-group study involved 79 community-dwelling older adults with physical frailty or locomotive syndrome assigned to an intervention group (n = 40) with the HAL lumbar type exercise program or a control group (n = 39) without the exercise program. The intervention group underwent trunk training (including trunk and hip flexion, standing and sitting from a single sitting position, and squats) and gait training (treadmill and parallel bars) twice a week for 5 weeks while wearing the HAL lumbar type. The 10-m usual and maximum walking speeds, Timed Up and Go test results, 5-times chair-standing test results, 5-question Geriatric Locomotive Function Scale (GLFS-5) scores, body-fat percentage, and muscle mass were measured before and after the intervention and analyzed using the intention-to-treat method. ResultsThe intervention (23 % male; mean age, 74.7 ± 4.7 years) and control (21 % male; mean age, 75.1 ± 4.1 years) groups did not differ significantly in baseline characteristics. Seventy-seven participants completed the program; two withdrew for personal reasons. The mean difference (standard error) between the groups for the primary outcome (usual walking speed) was 0.35 (0.04) m/s; the time-by-group interaction was significant (p < 0.001). Secondary outcomes (maximum walking speed, Timed Up and Go test results, 5-times chair-standing test results, and GLFS-5 scores) significantly improved in the intervention group. Body composition was unchanged in both groups. ConclusionsA 5-week exercise program using the HAL lumbar type is a promising option for community-dwelling older adults with limited mobility who do not require nursing care, resulting in clinically meaningful improvements in most physical functions within a short period.

Lyapunov stability of suspension bridges in turbulent flow

In the era of sleek, super slender suspension bridges, facing the issue of stability against dynamic wind actions represents an increasingly complex challenge. Despite the significant progress over the last decades, the impact of atmospheric turbulence on bridge stability remains partially not understood, evoking the need for innovative research approaches. This study aims to address a gap in current research by investigating the random flutter stability associated with variations in the angle of attack due to turbulence, which has not formally been addressed yet. The present investigation employs the 2D rational function approximation model to express self-excited forces in a turbulent flow. The application of this type of models to bridge dynamics yields a viscoelastic coupled dynamic system characterized by memory effects and driven by broad-band long-time-scale noise, described here by a linear homogeneous time-variant differential equation, which shows apparent nonlinear features, and which has rarely been matter of research. Utilizing a Monte Carlo methodology, this work innovates in applying the largest Lyapunov exponent (LE) and the moment Lyapunov exponents (MLE) to study bridge random flutter stability. The calculation of LE and MLE under diverse turbulent wind conditions uncovers lower flutter stability than without turbulence effects. In most cases, sample and low-order p-th moment stability thresholds closely align with the bridge dynamic response pattern; therefore, the flutter critical wind speed is unequivocal. However, under certain turbulence scenarios, it is necessary to resort to MLE for a complete description of stability, evoking some additional consideration of which statistical moments should be considered for the engineering assessment of the flutter limit. Finally, this work provides a qualitative insight into the instability mechanisms by approximating the random parametric excitation with a sinusoidal gust and evaluating the time-periodic system stability via Floquet theory.

A simple approach for the computation of Lyapunov–Floquet transformations for general time-periodic systems

A simple approach for the computation of Lyapunov–Floquet transformations for general time-periodic systems

Dynamic stability of the Mindlin-Reissner plate using a time-modulated axial force

A time-periodic axial force acting on a continuous structure can be destabilized by parametric excitation. Moreover, it is capable of increasing the equivalent damping and shortening the transient vibrations. In this work, this concept is extended, and dynamic stability of a Mindlin-Reissner plate is analyzed. The FE formulation for the four-node plate element is derived by employing the variational approach including the action of an axial force. The stability of the time-periodic system is evaluated both numerically and analytically, using Floquet theory and first-order approximation based on the averaging method, respectively. The influence of plate length, thickness, and aspect ratio on dynamic stability is highlighted. It is demonstrated that the instability tongue at a parametric combination resonance frequency of the summation type is shifted toward higher axial force amplitudes by increasing the plate width and decreasing the plate length. Alternatively, the axial force acting in the vicinity of a parametric combination frequency of the difference type shows a parametric antiresonance which is maximized by exactly the opposite tuning of the plate design. This guideline is important when plate design under the action of a harmonic axial force is considered.

Principal Spectral Theory of Time-Periodic Nonlocal Dispersal Cooperative Systems and Applications

Principal Spectral Theory of Time-Periodic Nonlocal Dispersal Cooperative Systems and Applications

Amplification in parametrically-driven resonators near instability based on Floquet theory and Green’s functions

Here we use Floquet theory to calculate the response of parametrically-driven time-periodic systems near the onset of parametric instability to an added external ac signal or white noise. We provide new estimates, based on the Green’s function method, for the response of the system in the frequency domain. Furthermore, we present novel expressions for the power and noise spectral densities. We validate our theoretical results by comparing our predictions for the specific cases of a single degree of freedom parametric amplifier and of the parametric amplifier coupled to a harmonic resonator with the numerical integration results and with analytical approximate results obtained via the averaging method up to second order.

Linear time periodic system approximation based on Floquet and Fourier transformations for operational modal analysis and damage detection of wind turbine

Operational Modal Analysis (OMA) identifies modal properties of mechanical structures from vibration data collected from a few sensors under operation conditions. These methods are widely used to monitor civil engineering structures that are modeled as time-invariant systems. However, when dealing with wind turbines and rotating machines, many dedicated OMA techniques were developed to deal with the time-periodic behavior. Existing methods pre-process the data to adapt them to classical identification techniques. Yet, these methods present limitations as either requiring a high number of measured rotation periods, assuming the assumption of an isotropic rotor (i.e. undamaged), or the knowledge of the rotational speed. This work proposes to lift these difficulties by proving that the application of the classical system identification methods can produce meaningful estimates for anisotropy monitoring. This observation is based on directly approximating the time-periodic dynamic behavior of the wind turbine as a properly defined time-invariant system under periodic inputs. It results in the possibility of using classical identification methods without modification to retrieve the system matrices of the approximated time-invariant system. This approach does not require knowing the rotor speed, requiring relatively fewer measurements and it is not restricted to isotropic rotors. The identified modes can be used reliably for the monitoring of operating wind turbines and more especially for fault detection, at the expense of losing a part of the complete description of the periodic system. The resulting anisotropy monitoring approach and its capacities are illustrated in two cases. Firstly, on an academic model of a wind turbine and then on an aero-servo-elastic numerical model of a rotating 10 MW wind turbine to demonstrate the ability of the method to deal with realistic and representative data. It is shown for the latest case, from sensors located on the blades of the wind turbine, the approach is able to identify correctly the system properties (frequencies and mode shapes) and is also able to detect efficiently a fault on a blade.

On the effects of rotor induced vibrational stability on helicopter flight dynamics

This article investigates vibrational stabilization effects in rotorcraft flight dynamics. This study is motivated by recent results in flapping-wing flight, which showed that the time-varying aerodynamic and inertial loads due to the insect wing periodic motion induce a vibrational stabilization mechanism in hover. The dynamics of flapping-wing flyers and rotary-wing vehicles are both described by time-periodic systems so vibrational stabilization mechanisms can also have an effect on stability characteristics of rotary-wing vehicles. The article extends the use of the harmonic decomposition method to vibrational stability analysis of rotorcraft. Two cases are considered: vibrational stability due blade imbalance at hover, and vibrational stability due to number-of-blades-per-rotor-revolution (Nb\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_b$$\\end{document}/rev) in high-speed forward flight. Results show that while vibrations induced by rotor blade imbalance do not stabilize the hovering dynamics of a helicopter, these vibrations can still have a significant effect on the hovering dynamics. Rotor blade imbalance results in a symmetric effect on the roll and pitch axes, in that it tends to decrease the frequency of the subsidence modes of the hovering cubic, while the unstable oscillatory modes tend to increase in frequency and decrease in damping (destabilizing effect). On the other hand, the yaw/heave dynamics are relatively unaffected compared to the lateral and longitudinal axes. Moreover, Nb\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_b$$\\end{document}/rev rotor loads in forward flight are shown to reduce the damping of the coupled roll/pitch oscillation mode.

Cuplength estimates for time-periodic measures of Hamiltonian systems with diffusion

We show how methods from Hamiltonian Floer theory can be used to establish lower bounds for the number of different time-periodic measures of time-periodic Hamiltonian systems with diffusion. After proving the existence of closed random periodic solutions and of the corresponding Floer curves for Hamiltonian systems with random walks with step width 1/n for every n∈N\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\in \\mathbb {N}$$\\end{document}, we show that, after passing to a subsequence, they converge in probability distribution as n→∞\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n\\rightarrow \\infty $$\\end{document}. Besides using standard results from Hamiltonian Floer theory and about convergence of tame probability measures, we crucially use that sample paths of Brownian motion are almost surely Hölder continuous with Hölder exponent 0<α<12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0<\\alpha <\\frac{1}{2}$$\\end{document}.

Propagation Dynamics of Forced Pulsating Waves for a Time Periodic Lotka-Volterra Cooperative System with Nonlocal Effects in Shifting Habitats

Propagation Dynamics of Forced Pulsating Waves for a Time Periodic Lotka-Volterra Cooperative System with Nonlocal Effects in Shifting Habitats

Construction of a Contraction Metric for Time-Periodic Systems Using Meshless Collocation

Construction of a Contraction Metric for Time-Periodic Systems Using Meshless Collocation

A generic impulsive controller for Hamiltonian time-independent systems

In a recent work Briozzo (2021) the author introduced an impulsive Floquet controller for periodic orbits in time-periodic Hamiltonian systems, which expresses the control law analytically in terms of the linearized dynamics about the reference orbit and makes full use of the center manifold enhancing performance by minimizing the energy of the actual orbit in the co-moving frame of the reference one. The purpose of the present work is to introduce an equivalent controller for Hamiltonian linear time-periodic systems obtained by linearization of a general time-independent Hamiltonian one about a periodic orbit, so incorporating the presence of a shear manifold associated to energy conservation and the ensuing non-isolation of periodic orbits. Like its preceding version, the controller defines a target subspace akin to the sliding surface of sliding mode controllers, onto which the system state vector is repeatedly sent by control impulses, and is generic in the sense that the target subspace and the control law are explicitly given for any possible decomposition of state space into a shear manifold and saddle, centre, or saddle-focus ones.

A Design Method to Eliminate Sub Synchronous Response in Automotive Turbochargers utilizing Nonlinear Dynamics of Time Periodic Systems

The present work introduces a methodology for the dynamic design evaluation of high-speed rotors, applying nonlinear dynamics of time periodic systems. The paper focuses on the definition of design variables so as the system to avoid sub synchronous components in the response. The response of an unbalanced turbocharger rotor mounted on oil bearings with wire mesh dampers (WMDs) is evaluated with an efficient collocation method coupled to the pseudo arc length continuation to evaluate response limit cycles in the entire range of the rotating speed, which acts as bifurcation parameter. The specific system is used to demonstrate the method without loss of generality. The analytical model of the WMD component is implemented directly from the literature, while rigid rotor model and short bearing approximations are used for the rest components. Floquet theory is applied in the non-autonomous dynamic system and the stability characteristics of the response limit cycles are evaluated through Floquet multipliers, the magnitude of which act in the algorithm as stability index. A sensitivity analysis is performed at first to evaluate the correlation between WMD key design parameters and the time response of the system.A multi objective optimization method is embedded to set Floquet multipliers at specific values; in this way the response limit cycles retain stability and periodicity, avoiding any type of bifurcation which would render sub-synchronous component. Acceptable sets for design variables of journal bearings and WMDs are defined by multi-objective optimization and these are verified in efficiency by evaluating the response of the system by time integration, as a virtual experiment, for several operating conditions. The method requires severely lower computational time and capacity to render an acceptable design compared to the conventional design of experiment DoE procedure, and it is not limited on the analytical models of rotor, bearing, or other component.

Propagation dynamics of nonlocal dispersal competition systems in time-periodic shifting habitats

This paper is concerned with the propagation dynamics of the time periodic Lotka-Volterra competition systems with nonlocal dispersal in a shifting habitat. We first obtain three types of time-periodic forced waves connecting the extinction state to the co-existence state, itself and the semi-trivial state, which describe the conversion from the state of two aboriginal co-existent competing species, two invading alien competitors, and a saturated aboriginal competitor with another invading alien competitor to the extinction state, respectively. This provides a comprehensive explanation of the point-wise extinction dynamics of these two competing species under such a time-periodic worsening habitat. Then, we establish the spreading properties of the associated Cauchy problem depending on the range of the shifting speed. More specifically, we give a complete description on the threshold values for the extinction as well as persistence (by moving with asymptotic speed). Our results reveal the possibility that a competitively weaker species with a much faster spreading speed can drive a competitively stronger species with a slower spreading speed to extinction. The discussion in this paper applies to both cases of weak competition and strong-weak competition. In particular, we need to point out that some combined effects of nonlocal dispersal, two-variable coupling and time-periodic shifting heterogeneity in this system pose extra difficulties in mathematical treatment, which are dealt with by introducing new approaches.

Frequency Scanning of Weakly Damped Single-Phase VSCs With Chirp Error Control

The chirp sweep is a go-to wide-band impedance measurement technique when speed and simplicity are of main concern. Additionally, the time-frequency trait of chirp scans provide unique benefits for systems exhibiting frequency couplings - a phenomenon often encountered in single-phase VSCs. Unfortunately, time domain interpretation of chirp responses are inaccurate if the VSC-based system exhibits weak damping, as the transient response induced by the chirp cannot be safely neglected. We quantify this error for linear(ised) time-invariant and time-periodic systems, with impedance representations of scalar transfer functions and harmonic transfer functions, respectively. An observer termed the Multiple Chirp Reference Frame Filter is proposed which enables real-time estimation of the harmonic transfer functions and their corresponding chirp errors. By controlling the relative errors to negligible values, the chirp exhibits low rate around resonances and high rate elsewhere. An experimental admittance sweep of a single-phase STATCOM operated by dispatchable Virtual Oscillator Control, consolidates the proposed approach as a simple frequency scan technique for weakly damped and frequency coupled systems.

Coexistence and competitive exclusion in a time-periodic Lotka-Volterra competition-diffusion system

The evolutionary impact of both temporal periodicity and spatial heterogeneity on population ecology is a challenging problem. Hutson et al. (2001) [12] and Bai et al. (2022) [2] studied the effects of diffusion rates on the dynamics of a time-periodic Lotka-Volterra competition-diffusion system with identical interspecific competition abilities. In this paper, we consider the case of different interspecific competition coefficients. The obtained results can be divided into two groups. The first part focuses on the interplay between the diffusion intensities and the interspecific competition coefficients on the dynamics in the weak competition case. We provide some sufficient conditions on coexistence and competitive exclusion. The second part considers the dynamics for fixed diffusion coefficients and varying competition coefficients. We not only provide a complete classification on the dynamics when one of the interspecific competition coefficients is small, but also show the multiple coexistence periodic patterns by applying the bifurcation method.

Flow control of a plunging cylinder based on resolvent analysis

We design an open-loop active flow control for separated flows around a plunging circular cylinder based on resolvent analysis. The cylinder is plunging at a Strouhal number of 0.36 and a Reynolds number of 500. A linear time-periodic system for control is obtained by linearizing the non-inertial incompressible vorticity equation in the cylinder-fixed frame about a time-averaged base flow. Using the Lyapunouv–Floquet transformation, the linear time-periodic system is transformed into a similar linear time-invariant system, whose resolvent is analysed to obtain an optimal actuating Strouhal number of 0.1464 for the transformed linear system. Simulations show that the active control with tangential actuations is capable of reducing the lift fluctuation by up to 25.7 % when the flow is actuated near the predicted harmonic and subharmonic frequencies.