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1.
In almost every ecological system, growth of various interacting species evolve in different time scales and the implementation of this time scale difference in the corresponding mathematical model exhibits some rich and complex oscillatory dynamics. In this article, we consider a predator–prey model with Beddington–DeAngelis functional response in which the prey reproduction is affected by the predation induced fear and its carry-over effect. Considering the growth of prey species occurs on a faster time scale than that of predator, the proposed system reduces to a ‘slow–fast predator–prey’ system. Using the geometric singular perturbation theory and asymptotic expansion technique, we investigate the system both analytically and numerically, and observe a wide range of rich and complex dynamics such as canard cycles (with or without head) near the singular Hopf-bifurcation threshold and relaxation oscillation cycles. The system experiences a canard explosion through which a rapid transition from small amplitude limit cycle to large amplitude limit cycle occurs in a tiny parametric interval. These types of complex oscillatory dynamics are absent in non slow–fast systems. Furthermore, it is shown that the interplay between fear and its carry-over effect, and the variation of time scale parameter may lead to a regime shift of the oscillatory dynamics. We also study the impact of fear and its carry-over effect on the properties of long transient dynamics. Thus our study provides some valuable biological insights of a slow–fast predator–prey system which will aid in understanding the interplay between fear and its carry-over effect.  相似文献   
2.
We establish a two timescale asymptotics of the weakly compressible Stokes system which has dissipation of order ε>0. For any L2 initial data, over time scale of order 1, the solutions of the weakly compressible Stokes system converge strongly to those of the acoustic system as ε0. Over time scale of order 1/ε, the limit system is the incompressible Stokes system with the initial data projected on the incompressible mode. For the periodic domain, the convergence is weak due to the fast oscillation generated by acoustic waves. For the Navier-slip boundary condition with the reciprocal of slip length being square of the Knudsen number, the acoustic waves are damped by the viscous boundary layer, and consequently the strong convergence is justified.  相似文献   
3.
The purpose of this paper is to describe the oscillatory properties of second‐order Euler‐type half‐linear differential equations with perturbations in both terms. All but one perturbations in each term are considered to be given by finite sums of periodic continuous functions, while coefficients in the last perturbations are considered to be general continuous functions. Since the periodic behavior of the coefficients enables us to solve the oscillation and non‐oscillation of the considered equations, including the so‐called critical case, we determine the oscillatory properties of the equations with the last general perturbations. As the main result, we prove that the studied equations are conditionally oscillatory in the considered very general setting. The novelty of our results is illustrated by many examples, and we give concrete new corollaries as well. Note that the obtained results are new even in the case of linear equations.  相似文献   
4.
格栅-空腔流动会引发流场自激振荡现象,产生结构振动及噪声问题.研究此类现象的形成机理对相关设备的减振降噪设计具有重要意义.目前已知这种现象是在流场正逆向两种扰动的耦合作用下形成的,但上述两种扰动的形成机理尚未明确.针对该问题,建立了格栅-空腔流动数值模型,并进行非稳态数值模拟.通过分析压力振荡数据及流场结构演化过程,对两种扰动的形成过程进行了研究.研究结果表明,正逆向两种扰动的形成均与格栅间隔中形成的小尺度涡团有关.上游小尺度涡团从格栅间隔中依次脱离并聚集演化为大尺度涡团,形成该流动系统的正向扰动.下游小尺度涡团脱离格栅间隔激发的逆向扰流构成该流动系统的逆向扰动,并对正向扰动产生持续的正反馈作用.  相似文献   
5.
In this paper, we consider the Sturm–Liouville equation with the jump conditions inside the interval (0,π). The inverse problem is studied, which consists in recovering operator coefficients from two spectra, corresponding to different boundary conditions. We prove the uniqueness theorem and provide necessary and sufficient conditions for solvability of the inverse problem. We also obtain the oscillation theorem for the eigenfunctions of the considered discontinuous boundary value problem.  相似文献   
6.
超疏水表面液滴的振动特性与接触线的移动、液滴体积、基底振幅等因素密切相关.本文在基底振幅较小且恒定的条件下,研究了超疏水表面液滴的共振振幅、模式区间、共振频率等振动特性及其与液滴体积(20—500μL)的关系.此外,将基于一般性疏水表面建立的Noblin共振频率计算模型应用于超疏水表面,并提出“虚驻点”的概念,借此对模型进行了误差分析和修正.研究表明:1)共振时,液滴高度变化率即比振幅随体积增大而增大,随阶数增大而减小;2)各模式区间的起止频率首尾相接,其范围随体积增大而减小;3)液滴体积越大,共振频率越小,随着阶数增大,共振频率f与体积V的关系趋于f-V–0.4,不同于一般性疏水表面上的f-V–0.5;4)直接应用Noblin模型计算共振频率会产生较大误差,主要原因在于液滴表面波波段数量统计存在较大偏差,而修正后的模型可以准确计算超疏水表面大体积液滴的共振频率.  相似文献   
7.
随着水土资源环境日益恶化,监测氨氮量对水土的污染程度也备受关注。为了准确测定铝灰渣浸出液中的氨氮量,实验对振荡方法、振荡时间、固液比、试液过滤方式、纳氏试剂加入量以及测定干扰因素进行了研究。确定了以翻转振荡为前处理方式,最佳振荡时间为14 h,固液比为1:10,最佳纳氏试剂加入量为1.0 mL,通过改善过滤方式,降低了空白值。由实验结果可知:在试验范围内,F-对氨氮量的测定不产生干扰;对于浸出液中Cl-、Al3+和Ca2+浓度高的样品,可通过移取稀释液2.00 mL,加入1.0 mL酒石酸钾钠溶液(500 g/L),即可消除其干扰。运用纳氏试剂分光光度法测定铝灰渣浸出液中的氨氮量,得到氨氮标准曲线线性相关系数为0.9998,方法检出限为0.39 mg.L-1,RSD(n=6)<5%,回收率在94.7%~105%之间。本方法简单快速,精密度高,且具有较低的检出限,适用于大批量铝灰铝渣等固体废物浸出液中氨氮量的测定。  相似文献   
8.
Zilu Cao 《中国物理 B》2022,31(11):118701-118701
Although the significant roles of magnetic induction and electromagnetic radiation in the neural system have been widely studied, their influence on Parkinson's disease (PD) has yet to be well explored. By virtue of the magnetic flux variable, this paper studies the transition of firing patterns induced by magnetic induction and the regulation effect of external magnetic radiation on the firing activities of the subthalamopallidal network in basal ganglia. We find: (i) The network reproduces five typical waveforms corresponding to the severity of symptoms: weak cluster, episodic, continuous cluster, episodic, and continuous wave. (ii) Magnetic induction is a double-edged sword for the treatment of PD. Although the increase of magnetic coefficient may lead the physiological firing activity to transfer to pathological firing activity, it also can regulate the pathological intensity firing activity with excessive β-band power transferring to the physiological firing pattern with weak β-band power. (iii) External magnetic radiation could inhibit continuous tremulous firing and β-band power of subthalamic nucleus (STN), which means the severity of symptoms weakened. Especially, the bi-parameter plane of the regulation region shows that a short pulse period of magnetic radiation and a medium level of pulse percentage can well regulate pathological oscillation. This work helps to understand the firing activity of the subthalamopallidal network under electromagnetic effect. It may also provide insights into the mechanisms behind the electromagnetic therapy of PD-related firing activity.  相似文献   
9.
Tao Li 《中国物理 B》2022,31(9):90502-090502
Studies of sustained oscillations on complex networks with excitable node dynamics received much interest in recent years. Although an individual unit is non-oscillatory, they may organize to form various collective oscillatory patterns through networked connections. An excitable network usually possesses a number of oscillatory modes dominated by different Winfree loops and numerous spatiotemporal patterns organized by different propagation path distributions. The traditional approach of the so-called dominant phase-advanced drive method has been well applied to the study of stationary oscillation patterns on a network. In this paper, we develop the functional-weight approach that has been successfully used in studies of sustained oscillations in gene-regulated networks by an extension to the high-dimensional node dynamics. This approach can be well applied to the study of sustained oscillations in coupled excitable units. We tested this scheme for different networks, such as homogeneous random networks, small-world networks, and scale-free networks and found it can accurately dig out the oscillation source and the propagation path. The present approach is believed to have the potential in studies competitive non-stationary dynamics.  相似文献   
10.
法诺共振是物理体系中普遍存在的一种非对称共振现象,它最早起源于量子物理,其微观图像是原子谱线中窄的分离态与宽的连续态之间的相干干涉.本文利用经典力学体系中两个弹簧振子的耦合,使其中一个弹簧振子受到周期性外力的驱动,成功类比了量子力学中的法诺共振现象.通过分析每个弹簧振子的动力学方程,严格求解它们的振动公式,从而得到每个弹簧振子的振幅和位相与外部驱动力频率之间的关系.结果表明,耦合体系中受外力驱动的那个弹簧振子既可以发生非对称的法诺共振,又可以发生对称的洛仑兹共振,而另一个弹簧振子只能发生洛仑兹共振.本文的推导与分析能够使读者更好地理解法诺共振现象及其激发条件.  相似文献   
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