Existence of periodic solutions for the nonlinear functional differential equation in the lossless transmission line model

doi:10.1088/1674-1056/21/1/010202

Abstract We study a time delay equation for the lossless transmission line model. Under suitable conditions, by using the continuation theorem of the coincidence degree theory, the existence of the periodic solution for the nonlinear functional differential equation is obtained.

Keywords: periodic solution time delay nonlinearity coincidence degree

Received: 11 July 2011
Revised: 01 September 2011
Accepted manuscript online:

PACS:	02.30.Hq	(Ordinary differential equations)
	02.30.Ks	(Delay and functional equations)
	02.30.Sa	(Functional analysis)
	02.30.Tb	(Operator theory)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11071075).

Cite this article:

Wang Na(汪娜) Existence of periodic solutions for the nonlinear functional differential equation in the lossless transmission line model 2012 Chin. Phys. B 21 010202

[1]	Kuang Y 1993 Delay Differential Equations with Applications in Population Dynamical System (New York: Academic Press)
[2]	Komanovskii V B and Nosov V R 1986 Stability of Functional Differential Equations (London: Academic Press)
[3]	Mo J Q 1993 J. Math. Anal. Appl. 178 289
[4]	Mo J Q 1989 Sci. China Ser. A 32 1306
[5]	Mo J Q and Lin W T 2005 Acta Math. Appl. Sin. 21 101 (in Chinese)
[6]	Mo J Q, Zhang W J and He M 2007 Acta Math. Sci. 27 777
[7]	Mo J Q, Zhu J and Wang H 2003 Prog. Nat. Sci. 13 768
[8]	Mo J Q 2009 Chin. Phys. Lett. 26 010204
[9]	Mo J Q 2009 Acta Phys. Sin. 58 693 (in Chinese)
[10]	Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese)
[11]	Mo J Q, Lin W T and Wang H 2007 Prog. Nat. Sci. 17 230
[12]	Mo J Q and Lin W T 2008 Chin. Phys. B 17 370
[13]	Mo J Q and Lin W T 2008 Chin. Phys. B 17 743
[14]	Lu S P and Ge W G 2003 Nonlinear Analysis 54 1285
[15]	Liu B W and Hang L H 2006 Acta Math. Sin. (Chin. Series) 49 1347 (in Chinese)
[16]	Liu B W and Huang L H 2006 J. Math. Anal. Appl. 322 121
[17]	Liu X P, Jia M and Ren R 2007 Math. Sci. Acta A 27A 037 (in Chinese)
[18]	Zhang L S, Cai L and Feng C W 2011 Acta Phys. Sin. 60 030308 (in Chinese)
[19]	Wang N and Ni M K 2011 Acta Phys. Sin. 60 050203 (in Chinese)
[20]	Hale J 1977 Theory of Functional Differential Equations (New York: Springer)
[21]	Gaines R E and Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations (Berlin: Springer)
[22]	Lu S P and Ge W G 2005 J. Sys. Sci. Math. Scis. 25 216 (in Chinese)

[1]	Hopf bifurcation and phase synchronization in memristor-coupled Hindmarsh-Rose and FitzHugh-Nagumo neurons with two time delays Zhan-Hong Guo(郭展宏), Zhi-Jun Li(李志军), Meng-Jiao Wang(王梦蛟), and Ming-Lin Ma(马铭磷). Chin. Phys. B, 2023, 32(3): 038701.
[2]	Effect of autaptic delay signal on spike-timing precision of single neuron Xuan Ma(马璇), Yaya Zhao(赵鸭鸭), Yafeng Wang(王亚峰), Yueling Chen(陈月玲), and Hengtong Wang(王恒通). Chin. Phys. B, 2023, 32(3): 038703.
[3]	Influence of optical nonlinearity on combining efficiency in ultrashort pulse fiber laser coherent combining system Yun-Chen Zhu(朱云晨), Ping-Xue Li(李平雪), Chuan-Fei Yao(姚传飞), Chun-Yong Li(李春勇),Wen-Hao Xiong(熊文豪), and Shun Li(李舜). Chin. Phys. B, 2022, 31(6): 064201.
[4]	Generation of mid-infrared supercontinuum by designing circular photonic crystal fiber Ying Huang(黄颖), Hua Yang(杨华), and Yucheng Mao(毛雨澄). Chin. Phys. B, 2022, 31(5): 054211.
[5]	Review on typical applications and computational optimizations based on semiclassical methods in strong-field physics Xun-Qin Huo(火勋琴), Wei-Feng Yang(杨玮枫), Wen-Hui Dong(董文卉), Fa-Cheng Jin(金发成), Xi-Wang Liu(刘希望), Hong-Dan Zhang(张宏丹), and Xiao-Hong Song(宋晓红). Chin. Phys. B, 2022, 31(3): 033101.
[6]	Inferring interactions of time-delayed dynamic networks by random state variable resetting Changbao Deng(邓长宝), Weinuo Jiang(蒋未诺), and Shihong Wang(王世红). Chin. Phys. B, 2022, 31(3): 030502.
[7]	Bifurcation and dynamics in double-delayed Chua circuits with periodic perturbation Wenjie Yang(杨文杰). Chin. Phys. B, 2022, 31(2): 020201.
[8]	Finite-time Mittag—Leffler synchronization of fractional-order complex-valued memristive neural networks with time delay Guan Wang(王冠), Zhixia Ding(丁芝侠), Sai Li(李赛), Le Yang(杨乐), and Rui Jiao(焦睿). Chin. Phys. B, 2022, 31(10): 100201.
[9]	Measurement-device-independent quantum secret sharing with hyper-encoding Xing-Xing Ju(居星星), Wei Zhong(钟伟), Yu-Bo Sheng(盛宇波), and Lan Zhou(周澜). Chin. Phys. B, 2022, 31(10): 100302.
[10]	Anti-$\mathcal{PT}$-symmetric Kerr gyroscope Huilai Zhang(张会来), Meiyu Peng(彭美瑜), Xun-Wei Xu(徐勋卫), and Hui Jing(景辉). Chin. Phys. B, 2022, 31(1): 014215.
[11]	Microcrack localization using a collinear Lamb wave frequency-mixing technique in a thin plate Ji-Shuo Wang(王积硕), Cai-Bin Xu(许才彬), You-Xuan Zhao(赵友选), Ning Hu(胡宁), and Ming-Xi Deng(邓明晰). Chin. Phys. B, 2022, 31(1): 014301.
[12]	Delayed excitatory self-feedback-induced negative responses of complex neuronal bursting patterns Ben Cao(曹奔), Huaguang Gu(古华光), and Yuye Li(李玉叶). Chin. Phys. B, 2021, 30(5): 050502.
[13]	Modeling and dynamics of double Hindmarsh-Rose neuron with memristor-based magnetic coupling and time delay Guoyuan Qi(齐国元) and Zimou Wang(王子谋). Chin. Phys. B, 2021, 30(12): 120516.
[14]	Optical solitons supported by finite waveguide lattices with diffusive nonlocal nonlinearity Changming Huang(黄长明), Hanying Deng(邓寒英), Liangwei Dong(董亮伟), Ce Shang(尚策), Bo Zhao(赵波), Qiangbo Suo(索强波), and Xiaofang Zhou(周小芳). Chin. Phys. B, 2021, 30(12): 124204.
[15]	Stabilization strategy of a car-following model with multiple time delays of the drivers Weilin Ren(任卫林), Rongjun Cheng(程荣军), and Hongxia Ge(葛红霞). Chin. Phys. B, 2021, 30(12): 120506.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Existence of periodic solutions for the nonlinear functional differential equation in the lossless transmission line model

Cite this article:

Online attention