模擬大自然的現象是最為重要的研究領域之一，近幾年對於了解網路的結構和其動態變化有越來越多的認識，同步化〈synchronization〉現象是一種典型的群體行為，也是大自然界的一種基本行為[7]。，許多真實世界的問題都和網路同步化有密切的關係。在此篇論文中，我們利用數學軟體MATLAB，設計一種由Wenwu Yu, Jinde Cao, and Jinhu L [10] 提出之具有不同時間延遲性的一般線性混沌耦合系統〈a generally linearly hybrid coupled network with time-varying delay〉[10，12]的程式，並且應用在Lorenz equation, Rössler equation與Chua's circuit這三種不同系統所形成的複雜網路〈complex network〉，更進一步地利用數值結果來窺探其同步化的動態。在此特別強調，此程式設計廣泛地包含不同的節點(nodes)耦合結構、可應用不同的混沌動態系統以及我們可以計算對於具有時間延遲性質之系統的相關結果。

To simulate the phenomenon of nature is one of the most important research territories. In recent years, it has more and more understanding regarding the structure of network and its dynamic change. Synchronization is a kind of typical collective behavior and a basic motion in nature[7]. Moreover, many real-world problems have a close relationship with network synchronization. In this paper, we use mathematics software, MATLAB, to design a generally linearly hybrid coupled network with time-varying delay[10,12] that was proposed by Wenwu Yu, Jinde Cao, and Jinhu L [10] , and apply to complex networks that is formed with these three kind of different systems , Lorenz equation, Rössler equation and Chua' s circuit. Further, we use the value to observes its synchronization development. Especially, we emphasize that this program is designed widely to contain the different coupled structure of nodes and to be possible to apply the different chaos dynamic system. We may infer result regarding the network with time-varying.

[1]呂敏杰、嚴祖強，”Lorenz混沌電路之間段同步研究”，國立中山大學物理研究所，碩士論文，2001
[2] Chien-I Chen,and Chin-Lung Li, Median Approach to the Wavelet Transform Method for the Coupled Chaotic System with Neumann Boundary Conditions and its Synchronous Applications, 〈2010〉
[3] C.T.H. Baker, C.A.H. Paul, and D.R. Will , Issues in the numerical solution of evolutionary delay differential equations, Adv. Comp. Math., 3 (1995),pp. 171–196.
[4] D. Cheng, G. Chen, J. L , and X. Yu, Characterizing the synchronizability of small-world dynamical networks, IEEE Trans. Circuits Syst. I Regul. Pap., 51 (2004), pp. 787–796.
[5] D. J. Watts and S. H. Strogatz, Collective dynamics of ‘small-world’ networks, Nature, 393 (1998),pp. 440–442.
[6] G. Chen and J. L , A time-varying complex dynamical network models and its controlled synchronization criteria, IEEE Trans. Automat. Control, 50 (2005), pp. 841–846.
[7] G. Chen, J. L , and X. Yu, Chaos synchronization of general complex dynamical networks, Phys. A,334 (2004), pp. 281–302.
[8] G. Chen, J. Zhou, and Z. Liu, Global synchronization of coupled delayed neural networks and applications to chaotic CNN models, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 14 (2004), pp. 2229–2240.
[9] J. A. Lu, J. L , and J. Zhou, Adaptive synchronization of an uncertain complex dynamical network,IEEE Trans. Automat. Control, 51 (2006), pp. 652–656.
[10] Jinde Cao, Jinhu L , and Wenwu Yu,Global Synchronization of Linearly Hybrid Coupled Networks with Time-Varying, (2008), pp. 108–133.
[11] J. Cao and W. Wang, Synchronization in an array of linearly coupled networks with time-varying delay,Phys. A, 366 (2006), pp. 197–211.
[12] J. Cao, P. Li, and W. Wang, Global synchronization in arrays of delayed neural networks with constant and delayed coupling, Phys. Lett. A, 353 (2006), pp. 318–325.
[13] L.F. Shampine，S. Thompson,Solving Delay Differential Equations with dde23, (2000), pp. 1–5.
[14]Müstak E. Yalçin, and Serdar Özoguz,“ n-scroll chaotic attractors from a first-order time-delay differential equation”, American Institute of Physics,〈2007〉
[15] S. H. Strogatz, Exploring complex networks, Nature, 410 (2001), pp. 268–276.
[16] T. Chen and W. Lu, Synchronization of coupled connected neural networks with delays, IEEE Trans.Circuits Syst. I Regul. Pap., 51 (2004), pp. 2491–2503.