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Collective motion is a common phenomenum in nature, and needs to be well-understood. In this paper, we try to understand this phenomenum by using the generalized Couzin model with heterogenous time delays. Simulation is carried out by using LAMMPS secondary development. It is found that when the homogeneous delay time increases, patterns of the collective motion change from highly parallel to vortex motion. While for heterogenous time delays, the individuals with short delays tend to distribute at the front part of the cluster when the delays are approximately normally distributed. If the cluster is divided into two sub-clusters, the distribution of individuals with short delays changes from favouring the front of the cluster to back, as the delay difference between two sub-clusters increases.

Time-delay systems with delay-dependent coefficients arise from different disciplines, but methods and algorithms for stability analysis of this kind of systems are very few compared with the intensive ones for time-delay systems with delay-free coefficients. This paper presents three algorithms for calculating the spectral abscissa of these time-delay systems with the delay as a parameter, an index that determines the stability and the decaying rate of the systems. The key step of the proposed algorithms is the use of parametric continuation method to calculate the real part branches by solving initial value problems of an ordinary differential equation derived from the characteristic function, where the initial values of the initial value problems are chosen as the rightmost characteristic roots, or the second rightmost characteristic roots, and so on, and they are calculated by using the integration-based-stability-test method. The algorithms are particularly effective when the delay interval is short.

To summarize the nursing experience of treating pediatric fulminant myocarditis with extracorporeal membrane oxygenation (ECMO). The intensive care unit of our hospital treated 6 children with fulminant myocarditis with ECMO from 2019 to 2022. The main nursing measures included establishing an ECMO rescue team, preparing before initiation of ECMO, management of arterial and venous catheters, enteral nutrition support, reducing the risk of infection aggravation, anticoagulation management, prevention of bleeding and thrombosis, management of ECMO pump failure, and post-ECMO care. One child’s family abandoned treatment and left the hospital, while the other 5 children were transferred to the cardiovascular department after stable weaning from ECMO and continued treatment, with good condition, and eventually discharged. Pediatric fulminant myocarditis has a high mortality rate, but detailed evaluation and nursing care can improve the outcome of these patients.

High levels of fine particulate matter (PM2.5) is linked to poor air quality and premature deaths, so haze pollution deserves the attention of the world. As abundant inorganic components in PM2.5, ammonium nitrate (NH4NO3) formation includes two processes, the diffusion process (molecule of ammonia and nitric acid move from gas phase to liquid phase) and the ionization process (subsequent dissociation to form ions). In this study, we discuss the impact of meteorological factors, emission sources, and gaseous precursors on NH4NO3formation based on thermodynamic theory, and identify the dominant factors during clean periods and haze periods. Results show that aerosol liquid water content has a more significant effect on ammonium nitrate formation regardless of the severity of pollution. The dust source is dominant emission source in clean periods; while a combination of coal combustion and vehicle exhaust sources is more important in haze periods. And the control of ammonia emission is more effective in reducing the formation of ammonium nitrate. The findings of this work inform the design of effective strategies to control particulate matter pollution.

A two-wheeled vehicle balancing a passive inverted pendulum is analyzed based on an experimental device. The corresponding mechanical model is a wheeled double pendulum, where only the position of the lower pendulum is measured. The sampling effect of the digital control is modeled as a zero-order hold. It is shown that the stabilization of the upright position is possible by proper choice of the control parameters as function of the sampling period of the controller. The model can be applied to analyze the behavior of wheeled vehicles with passive human subjects standing on it. The results are demonstrated on small-scale experimental realization of the system.

A pendulum on a movable support has been used widely in the modeling of many mechanical systems, say, as the simplest model of gantry cranes. This paper presents a comparison study of the stability of the controlled pendulum with a delayed proportional- derivative feedback controller or a delayed derivative-acceleration feedback controller for sway reduction. Numerical calculation shows that the delay combinations and the sign combinations of the gains have important impact on the stability of the controlled pendulum. Although acceleration feedback is used few in applications compared with the widely used proportional-derivative feedback, the case when the delay in the acceleration feedback is double of the one in the derivative feedback can be particularly useful in enlarging the stable region in the gain plane, or in enlarging the stable delay interval if the feedback gains are fixed.

The outbreak of novel coronavirus pneumonia in Wuhan, Hubei Province, in 2019 and its rapid spread across the country caused severe public panic in China. The purpose of this study was to investigate the mental health problems of children’s chaperones at the emergency clinic during the coronavirus disease 2019 (COVID-19) outbreak and to analyze the related influencing factors. A total of 260 chaperones for children in the emergency department participated in this cross-sectional study through the questionnaire constellation platform. The survey period was from February to June 2021. Information collected included demographic data and mental health scales. The Self-Assessment Scale for Anxiety, the Self-Rating Scale for Depression, and the Pittsburgh Sleep Quality Index assessed anxiety, depression, and sleep quality, respectively. Logistic regression was used to analyze influential factors associated with mental health problems. The prevalence of depression, anxiety, and sleep disorders among family members accompanying children attending the emergency room was 41.54%, 20.00%, and 93.08%, respectively, with 21.54% of family members suffering from moderate sleep disorders. Univariate analysis showed that being in Wuhan or not during the city closure (X2 = 8.61, P < .01) was strongly associated with the occurrence of depression; female (X2 = 4.87, P = .03), working or not (X2 = 6.39, P = .01) and fear of going to the hospital (X2 = 7.80, P = .01) were key factors for the occurrence of anxiety symptoms; Knowledge of transmission routes and prevention of COVID-19 (X2 = 12.56, P = .03) was a key factor for sleep disorders; logistic stepwise regression analysis showed that fear of going to the hospital was a risk factor for anxiety symptoms (odds ratio = 2.51, P < .01, 95% confidence interval = 1.30–4.85). Our findings suggest that mental health problems were prevalent among family members accompanying children attending the emergency department during the COVID-19 outbreak, with a high prevalence of sleep disturbances in particular. Relevant factors included presence or absence in Wuhan during the outbreak closure, gender, work or absence, and fear of hospital visits. There is a need to focus on the mental health distress of the chaperones for children in the emergency department, and to provide timely intervention and diversion.

Tropospheric ozone (O3) pollution is becoming the primary obstacle to the improvement of air quality in China, especially in the Pearl River Delta (PRD) region. Because O3pollution episodes are closely related to synoptic weather patterns (SWPs), historical episodes (from 2006 to 2019) were classified according to SWPs using the Lamb‐Jenkinson method. Monitoring network and weather reanalysis data, emission inventories, and satellite retrievals were used to investigate the spatiotemporal characteristics and influences of O3pollution. It was found that easterly (P_E), anticyclone (P_A), and typhoon‐related (P_NE) SWPs accounted for 75% of all O3pollution episodes. In the PRD, the O3formation mechanism showed clear differences under different SWPs, which were affected by local emissions under P_A, whereas regional transmission dominated under P_E and P_NE. The O3peak concentration was strongly associated with temperature, solar radiation, and shifting of the sea‐land breeze. A delayed shift of land to sea breeze caused by SWPs often caused the O3peak to appear in the late afternoon. Finally, stepwise regression was used to explain individual meteorological parameters contributing to O3formation. It was found that the formation of O3pollution under P_E and P_NE was associated with increases in temperature and radiation, while P_A was mainly affected by the increase of the overnight accumulation of O3. This study advances our knowledge of the formation mechanism of O3pollution and provides scientific support for effective O3pollution control. In recent years, tropospheric ozone (O3) has become an important air pollutant hindering the improvement of air quality in the Pearl River Delta (PRD) region, China. In spite of the complicated nonlinear relationship between O3and its precursor, the variable synoptic weather patterns (SWPs), which control O3production and transportation, bring troubles to O3pollution control. To explore the influence of SWPs on spatiotemporal characteristics and internal causes of O3pollution, we objectively classified the historical episodes (from 2006 to 2019) and analyzed the meteorological factors, transmission paths of pollutants, and O3pollution characteristics under different SWPs. It was found that easterly (P_E), anticyclone (P_A), and typhoon‐related (P_NE) SWPs were the most common O3pollution weather systems. Generally, P_A mainly features local emission pollution, the cyclone circulation is conducive to the accumulation of ozone at night, resulting in high O3levels on the next day. P_E and P_NE tend to cause regional transmission pollution with unfavored meteorological conditions like the increase in temperature and radiation. Based on the findings, we constructed a multivariate linear regression model which can accurately predict the MDA8 O3in advance. This study provides a scientific support for O3pollution control. Historical O3episodes in the Pearl River Delta are classified according to synoptic weather patterns (SWPs)The O3formation mechanism shows clear differences under different SWPs and the dominant parameters are diagnosedThe anticyclone pattern is sensitive to overnight ozone accumulation, while the other patterns are sensitive to meteorological parameters Historical O3episodes in the Pearl River Delta are classified according to synoptic weather patterns (SWPs) The O3formation mechanism shows clear differences under different SWPs and the dominant parameters are diagnosed The anticyclone pattern is sensitive to overnight ozone accumulation, while the other patterns are sensitive to meteorological parameters

In this paper, we study the problem of stability test of neutral delay differential equations. Firstly we prove that the Mikhailov stability criterion and its equivalent integral form for ordinary differential equations hold for neutral delay differential equations in general form. The criteria are simple in form that is easy for numerical implementation. However, the criteria are characterized by an auxiliary function associated with the characteristic function, not by the characteristic function itself. To reduce the computational complexity, we further prove that a Mikhailov-type criterion in terms of the characteristic function holds. With this new criterion, the stability of a given neutral delay differential equation can be tested with a rough estimation of the testing integral. Thus, the computational complexity and computational cost can be greatly reduced. As two applications of these criteria, we firstly propose a numerical scheme for calculating the rightmost characteristic root(s) as well as the characteristic roots other than the rightmost roots of a given neutral delay differential equation, demonstrated with two examples. Then we derive a graphical stability criterion. With this graphical stability criterion, it is not required to know the exact curve of the Nyquist plot, but just to know whether the Nyquist plot encircles the origin of the complex plane or not.

Abstract: This paper focuses on the stability testing of fractional-delay systems. It begins with a brief introduction of a recently reported algorithm, a detailed demonstration of a failure in applications of the algorithm and the key points behind the failure. Then, it presents a criterion via integration, in terms of the characteristic function of the fractional-delay system directly, for testing whether the characteristic function has roots with negative real parts only or not. As two applications of the proposed criterion, an algorithm for calculating the rightmost characteristic root and an algorithm for determining the stability switches, are proposed. The illustrative examples show that the algorithms work effectively in the stability testing of fractional-delay systems.

Abstract: Periodic solutions occur commonly in linear or nonlinear dynamical systems. In some cases, the stability of a periodic solution holds if the rightmost characteristic root has negative real part. Based on the Lambert W function, this paper presents a simple algorithm for locating the rightmost characteristic root of periodic solutions of some nonlinear oscillators with large time delay. As application, the proposed algorithm is used to study the primary resonance and 1/3 subharmonic resonance of the Duffing oscillator under harmonic excitation and delayed feedback, as well as the control problem of the van der Pol oscillator under harmonic excitation by using delayed feedback, with a number of case studies. The main advantage of this algorithm is that though very simple in implementation, it works effectively with high accuracy even if the delay is large.

Abstract: This paper presents an investigation on the phenomenon of delayed bifurcation in time-delayed slow-fast differential systems. Here the two delayed’s have different meanings. The delayed bifurcation means that the bifurcation does not happen immediately at the bifurcation point as the bifurcation parameter passes through some bifurcation point, but at some other point which is above the bifurcation point by an obvious distance. In a time-delayed system, the evolution of the system depends not only on the present state but also on past states. In this paper, the time-delayed slow-fast system is firstly simplified to a slow-fast system without time delay by means of the center manifold reduction, and then the so-called entry-exit function is defined to characterize the delayed bifurcation on the basis of Neishtadt’s theory. It shows that delayed Hopf bifurcation exists in time-delayed slow-fast systems, and the theoretical prediction on the exit-point is in good agreement with the numerical calculation, as illustrated in the two illustrative examples.

Abstract: It begins with the study of damping representation of a linear vibration system of single degree of freedom (SDOF), from the view point of fractional calculus. By using the idea of stability switch, it shows that the linear term involving the fractional-order derivative of an order between 0 and 2 always acts as a damping force, so that the unique equilibrium is asymptotically stable. Further, based on the idea of stability switch again, the paper proposes a scheme for determining the stable gain region of a linear vibration system under a fractional-order control. It shows that unlike the classical velocity feedback which can adjust the damping force only, a fractional-order feedback can adjust not only the damping force, but also the elastic restoring force, and in addition, a fractional-order PD α control can either enlarge the stable gain region or narrow the stable gain region. For the dynamic systems described by integer-order derivatives, the asymptotical stability of an equilibrium is guaranteed if all characteristic roots stay in the open left half-plane, while for the systems with fractional-order derivatives, the asymptotical stability of an equilibrium is guaranteed if all characteristic roots stay within a sector in the complex plane. Analysis shows that the proposed method, based on the idea of stability switch, works effectively in the stability analysis of dynamical systems with fractional-order derivatives.

This paper presents a new approach, based on the center manifoldtheorem, to reducing the dimension of nonlinear time-delay systemscomposed of both stiff and soft substructures. To complete the reductionprocess, the dynamic equation of a delayed system is first formulated asa set of singular perturbed equations that exhibit dynamic behaviorevolving in two different time scales. In terms of the fast time scale,the dynamic equation of system can be converted into the standard formof a functional differential equation in critical cases, namely, to aform that can be treated by means of the center manifold theorem. Then,the approximated center manifold is determined by solving a series ofboundary-value problems. The center manifold theorem ensures that thedominant dynamics of the system is described by a set of ordinarydifferential equations of low order, the dimension of which is identicalto that of the phase space of slowly variable states. As an applicationof the proposed approach, a detailed stability analysis is made for aquarter car model equipped with an active suspension with a time delaycaused by a hydraulic actuator. The analysis shows that the dimensionalreduction is surprisingly effective within a wide range of the systemparameters.

The paper presents a simple approach to testifying the asymptotic stability and interval stability (robust stability against the change of system parameters in given intervals) for linear dynamic systems involving short time delays. The stability analysis starts with the study of the characteristic roots of a transcendental equation having exponential functions. By means of the Padé approximation to the exponential functions, the transcendental characteristic equation is approximated as an algebraic equation. Then, the test of asymptotic stability and interval stability of the system is completed in a very simple way. The stability analysis of a vibration system with short time delays in the feedback paths of displacement and velocity, taken as an example, is given in detail. The analysis and numerical examples indicate that the approach gives excellent accuracy for linear dynamic systems with short time delays.

Stability of a dynamical system may change from stable to unstable or vice versa, with the change of some parameter of the system. This is the phenomenon of stability switches, and it has been investigated intensively in the literature for conventional time-delay systems. This paper studies the stability switches of a class of fractional-delay systems whose coefficients depend on the time delay. Two simple formulas in closed-form have been established for determining the crossing direction of the characteristic roots at a given critical point, which is one of the two key steps in the analysis of stability switches. The formulas are expressed in terms of the Jacobian determinant of two auxiliary real-valued functions that are derived directly from the characteristic function, and thus, can be easily implemented. Two examples are given to illustrate the main results and to show an important difference between the fractional-delay systems with delay-dependent coefficients and the ones with delay-free coefficients from the viewpoint of stability switches.