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| Title: | 線性耦合系統之解的有界性
Boundedness of solutions of coupled systems with linear couplings |
| Authors: | 曾俊霖
TSENG, CHUN-LIN |
| Contributors: | 曾睿彬
Tseng, Jui-Pin
曾俊霖
TSENG, CHUN-LIN |
| Keywords: | 被動系統
半被動系統
耦合系統
有界性
passive system
semi-passive system
coupled system
boundedness |
| Date: | 2024 |
| Issue Date: | 2024-06-03 11:48:19 (UTC+8) |
| Abstract: | 在這篇論文中，我們利用與被動系統和半被動系統相關的理論來討論在線性耦合下耦合系統解的有界性。我們通過稍微放寬([6])中提出之semi-passivity定義的條件來修改其定義，然後建立相應的有界性理論。最後，利用本論文介紹的有界性理論，我們推導出了Lorenz系統、Chen系統、Lü系統、Stuart-Landau系統和線性mass-spring-damper系統解的有界性標準。
In this thesis, we discuss the boundedness of solutions for coupled systems under linear coupling by utilizing theories related to passive and semi-passive systems. We modify the definition of semi-passivity proposed in ([6]) by slightly relaxing its conditions and then establish the corresponding boundedness theory. Finally, with the boundedness theories introduced in this thesis, we derive the criteria of boundedness of solutions for Lorenz system, Chen system, Lü system, Stuart-Landau system, and linear mass-spring-damper system. |
| Reference: | [1]A. Y. Pogromsky, Passivity based design of synchronizing systems, International Journal of Bifurcation and Chaos, 8 (1998), pp. 295-319.
[2]A. Pogromsky, T. Glad and H. Nijmeijer, On diffusion driven oscillations in coupled dynamical systems, International Journal of Bifurcation and Chaos, 9 (1999), pp. 629-644.
[3]A. Pogromsky and H. Nijmeijer, Cooperative oscillatory behavior of mutually coupled dynamical systems, IEEE Trans. Circuits Syst. I, 48 (2001), pp. 152-162.
[4]A. Pogromsky, G. Santoboni and H. Nijmeijer, Partial synchronization: from symmetry towards stability, Physica D, 172 (2002), pp. 65-87.
[5]E. Steur and H. Nijmeijer, Synchronization in networks of diffusively time-delay coupled (semi-)passive systems, IEEE Trans. Circuits Syst. I, 58 (2011), pp. 1358-1371.
[6]Chih-Lun Chao, Semi-passivity and Synchronization in Linearly Coupled Systems, National Chiao Tung University, (2017), pp. 1-77.
[7]E. Steur, I. Tyukin and H. Nijmeijer, Semi-passivity and synchronization of diffusively coupled neuronal oscillators, Physica D, 238 (2009), pp. 2119-2128.
[8]Anes Lazri, Mohamed Maghenem, Elena Panteley and Antonio Loria, Global Uniform Ultimate Boundedness of Semi-Passive Systems Interconnected over Directed Graphs. 2023. hal-04298172.
[9]I.G. Polushin, D.J. Hill, A.L. Fradkov, Strict quasipassivity and ultimate boundedness for nonlinear control systems, in: Proceedings of the Fourth IFAC Symposium on Nonlinear Control Systems, NOLCOS’98, Enshede, The Netherlands, 1998.
[10]Xiwei Liu, Tianping Chen, Boundedness and synchronization of y-coupled Lorenz systems with or without controllers, Physica D 237 (2008), pp. 630–639.
[11]Wen-Xin Qin , Guanrong Chen, On the boundedness of solutions of the Chen system, J. Math. Anal. Appl. 329 (2007) 445–451.
[12]Chunlai Mu , Fuchen Zhang , Yonglu Shu and Shouming Zhou, On the boundedness of solutions to the Lorenz-like family of chaotic systems, Nonlinear Dyn (2012) 67:987–996.
[13]Fuchen Zhang , Xiaofeng Liao and Guangyun Zhang, On the global boundedness of the Lü system, Applied Mathematics and Computation 284 (2016) 332–339. |
| Description: | 碩士
國立政治大學
應用數學系
109751011 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0109751011 |
| Data Type: | thesis |
| Appears in Collections: | [Department of Mathematical Sciences] Theses
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