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Robust outer synchronization between two complex networks with fractional order dynamics
2. P. Butzer and U. Westphal, An Introduction to Fractional Calculus (World Scientific, Singapore, 2000).
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19. W. Sun, Y. Li, C. Li, and Y. Q. Chen, Asian J. Control 15, 1 (2013).
20. This is an iterative algorithm that performs a local averaging over neighbor nodes, similar to a diffusion process.
21. J. Zhou, J. Lu, and J. L, Automatica 44, 996 (2008).
24. The infectious diseases that spread across different communities provide an example of outer synchronization in the real world. Other applications can be found in Refs. 25 and 26 .
31. See Eq. (16) in Ref. 30. This equality does not hold for general nonlinear systems such as, e.g., the Lorenz system.
32. Specifically, we find sufficient and necessary conditions for the fractional-order differential equations governing the dynamics of the synchronization error, , to have a fixed point at .
33. Two systems A and B are in a generalized synchronization status when the state of the system B can be obtained as a deterministic transformation of the state of the system A .
34. I. Podlubny, Fractional Differential Equations (Academic, New York, 1999).
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52. For a matrix , with entries mi,j, i = 1,…,r, j = 1,…,k, we say that M is bounded if every entry is bounded, i.e., there exists a constant c such that |mi,j| < c for all i and j .
53. K. Diethelm, Electron. Trans. Numer. Anal. 5, 1 (1997).
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