Search Results (7)

Several types of linear and nonlinear singularly perturbed time-delay differential systems are considered. Asymptotic stability of the linear systems and asymptotic stability of the trivial solution of the nonlinear systems, valid for any sufficiently small value of the parameter of singular perturbation, are analyzed. For the stability analysis in the linear case, a partial exact slow–fast decomposition of the original system and an application of the Symmetric Matrix Riccati Equation method are proposed. Such an analysis yields parameter-free conditions, providing the asymptotic stability of the considered linear singularly perturbed time-delay differential systems for any sufficiently small value of the parameter of singular perturbation. Using the asymptotic stability results for the considered linear systems and the method of asymptotic stability in the first approximation, parameter-free conditions, guaranteeing the asymptotic stability of the trivial solution to the considered nonlinear systems for any sufficiently small value of the parameter of singular perturbation, are derived. Illustrative examples are presented. Full article

With the penetration of distributed resources into power distribution networks, power distribution networks are transforming into active distribution networks with a high proportion of distributed generations and power electronic equipment. Efficient modeling and simulation methods are essential to perform dynamic response analysis. In order to satisfy the fast/steady/slow multiple time-scale simulation requirements of active distribution networks, a fast/medium/slow time partition model and a network decoupling method for short line characteristic lines is proposed in this paper. Through the decomposition coordination simulation method, the network is decomposed into multiple regions that can be simulated in parallel. Based on the interconnection of fiber optic network cards, a multi-rate parallel simulation and synchronization strategy is proposed, which significantly improves the simulation speed of active distribution networks while ensuring simulation accuracy. The numerical experiments have been conducted based on a modified IEEE 33-bus and a PG&E 69-bus, and simulation results show the feasibility of the proposed method. The verification results of the example show that using adaptive variable-step-size multi-rate parallel simulation technology can increase the subnet computation-time balance rate and simulation acceleration ratio to 119.90% and 121.31% in the same rate-parallel mode. Full article

Compost amendments, apart from improving fertility and the general characteristics of agricultural soils, have known implications for global C cycling and sequestration in soils. Their effects are usually assessed via the quantification of soil organic carbon (SOC) pools, usually labile (fast) and recalcitrant (slow) pools, with varying intrinsic decomposition rates and distinct resident times. However, the real C-sequestration potential of organic additions to soil is still under discussion. In this study, a field trial and a lab incubation experiment were designed to study the C-sequestration mechanism in an agricultural Mediterranean soil. Soil with a history of C3 photosystem crop was amended with two maize composts from maize harvesting surpluses (C4 photosystem) with different maturity stages (AC: aged compost; NC: new, less mature compost). The evolution of SOM was monitored for 6 months using complementary analytical techniques, including analysis of stable C isotopes (IRMS), thermogravimetry (TG) and C-stock and priming effect (PE) modelling. Based on the natural C-isotope labelling, the proportion of new C was calculated. More than 50% of the C added to the soil with the compost was incorporated into the SOM in only 6 months. However, the application of maize compost did not always enhance soil C-sequestration capacity. The addition of compost caused a general PE, enhancing SOM decay and reducing the fast (labile) SOM mean residence time (MRT) (11.2 days). This was more pronounced with the addition of a higher dose of AC, causing a PE up to a 718%. On the other hand, a higher MRT (54.4 days) occurred in soils with NC applied, likely due to its deleterious effects, limiting heterotrophic activity. Despite that, the average MRT of the slow (recalcitrant) SOM pool was lower than usually reported. The application of higher doses of both composts generally showed greater MRT values compared to control (1.7 years vs. 3.8 and 2.9 years for NC and AC, respectively), leading to an increase in this more stable C pool and effective soil C sequestration. The results described in this work may help readers to better understand SOM dynamics and may be of use in designing appropriate management strategies for improving OM quantity and quality and to optimize C storage in Mediterranean soils. Full article

Since the famous slow–fast dynamical system referred to as the Hodgkin–Huxley model was proposed to describe the threshold behaviors of neuronal axons, the study of various slow–fast dynamical behaviors and their generation mechanisms has remained a popular topic in modern nonlinear science. The primary purpose of this paper is to introduce a novel transition route induced by the comprehensive effect of special rest spike bistability and timescale difference rather than a common bifurcation via a modified Chua’s circuit model with an external low-frequency excitation. In this paper, we attempt to explain the dynamical mechanism behind this novel transition route through quantitative calculations and qualitative analyses of the nonsmooth dynamics on the discontinuity boundary. Our work shows that the whole system responses may tend to be various and complicated when this transition route is triggered, exhibiting rich slow–fast dynamics behaviors even with a very slight change in excitation frequency, which is described well by using Poincaré maps in numerical simulations. Full article

Inhibiting the intestinal α-glucosidase can effectively control postprandial hyperglycemia for type 2 diabetes mellitus (T2DM) treatment. In the present study, we reported the binding interaction of betulinic acid (BA), a pentacyclic triterpene widely distributed in nature, on α-glucosidase and its alleviation on postprandial hyperglycemia. BA was verified to exhibit a strong inhibitory effect against α-glucosidase with an IC₅₀ value of 16.83 ± 1.16 μM. More importantly, it showed a synergistically inhibitory effect with acarbose. The underlying inhibitory mechanism was investigated by kinetics analysis, surface plasmon resonance (SPR) detection, molecular docking, molecular dynamics (MD) simulation and binding free energy calculation. BA showed a non-competitive inhibition on α-glucosidase. SPR revealed that it had a strong and fast affinity to α-glucosidase with an equilibrium dissociation constant (K_D) value of 5.529 × 10⁻⁵ M and a slow dissociation. Molecular docking and MD simulation revealed that BA bound to the active site of α-glucosidase mainly due to the van der Waals force and hydrogen bond, and then changed the micro-environment and secondary structure of α-glucosidase. Free energy decomposition indicated amino acid residues such as PHE155, PHE175, HIE277, PHE298, GLU302, TRY311 and ASP347 of α-glucosidase at the binding pocket had strong interactions with BA, while LYS153, ARG210, ARG310, ARG354 and ARG437 showed a negative contribution to binding affinity between BA and α-glucosidase. Significantly, oral administration of BA alleviated the postprandial blood glucose fluctuations in mice. This work may provide new insights into the utilization of BA as a functional food and natural medicine for the control of postprandial hyperglycemia. Full article

In this study, a singularly perturbed linear time-delay system of neutral type is considered. It is assumed that the delay is small of order of a small positive parameter multiplying a part of the derivatives in the system. This system is decomposed asymptotically into two much simpler parameter-free subsystems, the slow and fast ones. Using this decomposition, an asymptotic analysis of the spectrum of the considered system is carried out. Based on this spectrum analysis, parameter-free conditions guaranteeing the exponential stability of the original system for all sufficiently small values of the parameter are derived. Illustrative examples are presented. Full article

The motion control of a surface ship based on a four degrees of freedom (4-DoF) (surge, sway, roll, and yaw) maneuvering motion model is studied in this paper. A time-scale decomposition method is introduced to solve the path-following problem, implementing Rudder Roll Stabilization (RRS) at the same time. The control objectives are to let the ship to track a predefined curve path under environmental disturbances, and to reduce the roll motion at the same time. A singular perturbation method is used to decouple the whole system into two subsystems of different time scales: the slow path-following subsystem and the fast roll reduction subsystem. The coupling effect of the two subsystems is also considered in this framework of analysis. RRS control is only possible when there is the so-called bandwidth separation characteristic in the ship motion system, which requires a large bandwidth separation gap between the two subsystems. To avoid the slow subsystem being affected by the wave disturbances of high frequency and large system uncertainties, the $L_1$ adaptive control is introduced in the slow subsystem, while a Proportion-Differentiation (PD) control law is adopted in the fast roll reduction subsystem. Simulation results show the effectiveness and robustness of the proposed control strategy. Full article