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In this paper, we consider the non-autonomous semilinear impulsive differential equations with state-dependent delay. The approximate controllability results of the first-order systems are obtained in a separable reflexive Banach space, which has a uniformly convex dual. In order to establish sufficient conditions of the approximate controllability of such a system, we have used the theory of linear evolution systems, properties of the resolvent operator and Schauder’s fixed point theorem. Finally, we provide two concrete examples to validate our results. 相似文献
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In this paper, we concentrate on the spatiotemporal patterns of a delayed reaction‐diffusion Holling‐Tanner model with Neumann boundary conditions. In particular, the time delay that is incorporated in the negative feedback of the predator density is considered as one of the principal factors to affect the dynamic behavior. Firstly, a global Turing bifurcation theorem for τ = 0 and a local Turing bifurcation theorem for τ > 0 are given. Then, further considering the degenerated situation, we derive the existence of Bogdanov‐Takens bifurcation and Turing‐Hopf bifurcation. The normal form method is used to study the explicit dynamics near the Turing‐Hopf singularity. It is shown that a pair of stable nonconstant steady states (stripe patterns) and a pair of stable spatially inhomogeneous periodic solutions (spot patterns) could be bifurcated from a positive equilibrium. Moreover, the Turing‐Turing‐Hopf–type spatiotemporal patterns, that is, a subharmonic phenomenon with two spatial wave numbers and one temporal frequency, are also found and explained theoretically. Our results imply that the interaction of Turing and Hopf instabilities can be considered as the simplest mechanism for the appearance of complex spatiotemporal dynamics. 相似文献
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This paper firstly deals with finite time stability (FTS) of Riemann‐Liouville fractional delay differential equations via giving a series of properties of delayed matrix function of Mittag‐Leffler. We secondly study relative controllability of such type‐controlled system. With the help of the representation of solution, both Gram‐like type matrix and rank criterion are derived, which extend the corresponding results for linear systems. 相似文献
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Qing-Hua Ke Yue-Ming Zhou Yi-Jie Liao Jin-Tai Liang Yong Zhao Jia Tan Min Li Pei-Xiang Lu 《Frontiers of Physics》2021,16(5):52503
By numerically solving the three-dimensional time-dependent Schrödinger equation, we have invest-tigated multiphoton ionization of hydrogen atom in the two-color circularly polarized (TCCP) laser fields consisting of a strong 400 nm and a much weaker 800 nm pulses. Due to the presence of perturb-bative 800 nm laser pulse, sideband peaks emerge between the above-threshold ionization rings in the photoelectron momentum distributions. Our numerical results show that the sideband peaks exhibit one-lobe structure in the co-rotating TCCP laser fields, while it displays the three-lobe structure in the counter-rotating TCCP laser fields. Moreover, the photoelectron yield of sidebands in the co-rotating TCCP fields is much higher than those of the counter-rotating TCCP fields. These phenomena could be well explained from the perspective of the photon-absorption channels via the selection rules. In-terestingly, an obvious phase shift between the sidebands of different orders from the co-rotating and counter-rotating TCCP fields is observed. This shift indicates the helicity-dependent time delay in the one-photon continuum-continuum transition process. 相似文献
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本文提出了一种应用于光纤延时系统中实现光纤延时精密测量的新方法,用以提高光纤延时测量的精度和准确性.该方法以1064 nm激光调制信号作为光源,通过测量回波信号的幅值和相位信息得到被测通道的频率响应,采用快速傅里叶逆变换得到被测目标的延时信息,实现光纤延时测量.本文通过理论分析和延时测量实验对频域反射法与传统的时域测量方法进行对比,使用频域反射法在调制频率范围10—200 MHz,采样频率间隔0.5 MHz的实验条件下,实现了3.3 ps延时测量分辨率,并证明了该方法具有比时域方法更高的测量精度,测量结果的准确性更好. 相似文献
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The principal purpose of Ad-Hoc wireless networks is to increase service efficiency in terms of transmission scheduling and packet transfer rate. The approaches that assume frame unicity to satisfy a given set of packets minimize the end-to-end delay. However, they do not guarantee a maximum packet delivery rate due to the difficulty of establishing robust paths for packet transfer across nodes deployed in the network, especially in a three-dimensional (3D) environment. The objective is to minimize the end-to-end delay by ensuring the maximum delivery of packets to their destinations. Furthermore, the signal-to-interference-and-noise-ratio (SINR) model is considered to optimize transmission scheduling. In this paper, an optimal node coordinates optimization approach is proposed to extend two recently investigated schemes in the literature (S-RDSP and I-RDSP). The developed algorithms, named S-MPDR and I-MPDR, seek to reduce the end-to-end delay by delivering a collection of inserted packets over a 3D environment while also maximizing the delivery rate of these packets. Desirability functions are used to evaluate the network’s performance in various scenarios involving two different environments, Level 0 and Level 1. Numerical results demonstrate that the developed algorithms outperform both schemes in terms of end-to-end delay and packet delivery rate. In the Level 0 environment, the overall minimum delay and packet delivery rate scores provided by S-MPDR are increased by 28% and 88% compared to S-RDSP, respectively. In comparison, those provided by I-MPDR are increased by 24% and 16% compared to I-RDSP. Similarly, in the Level 1 environment, the scores provided by S-MPDR are increased by 25% and 100% compared to S-RDSP, respectively, while those provided by I-MPDR are increased by 23% and 25% compared to I-RDSP. 相似文献