SCIENCE CHINA Information Sciences, Volume 63 , Issue 3 : 132201(2020) https://doi.org/10.1007/S11432-019-9946-6

## Global Mittag-Leffler stability for fractional-order coupled systems on network without strong connectedness

• AcceptedMay 30, 2019
• PublishedFeb 10, 2020
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### Acknowledgment

This work was supported by National Natural Science Foundation of China (Grant No. 61873071) and Shandong Provincial Natural Science Foundation (Grant No. ZR2019MF027).

### References

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• Figure 3

(Color online) Response curves of (17) with the initial values $\textbf{\textit{Z}}_{1},\textbf{\textit{Z}}_{2}$, and $\textbf{\textit{Z}}_{3}$. (a) and (b) show the curves of states and control inputs of system (17).

• Table 1

Table 1Parameters used in the coupled system (16)

 Parameter Value Parameter Value Parameter Value Parameter Value Parameter Value Parameter Value $\alpha_{1}$ 0.17 $\beta_{1,1}$ 0 $\beta_{2,1}$ 0.1 $\beta_{3,1}$ 0.4 $\beta_{4,1}$ 0 $\beta_{5,1}$ 0 $\alpha_{2}$ 0.30 $\beta_{1,2}$ 0.1 $\beta_{2,2}$ 0 $\beta_{3,2}$ 0 $\beta_{4,2}$ 0 $\beta_{5,2}$ 0 $\alpha_{3}$ 0.46 $\beta_{1,3}$ 0 $\beta_{2,3}$ 0 $\beta_{3,3}$ 0 $\beta_{4,3}$ 0.2 $\beta_{5,3}$ 0.4 $\alpha_{4}$ 0.59 $\beta_{1,4}$ 0 $\beta_{2,4}$ 0 $\beta_{3,4}$ 0.2 $\beta_{4,4}$ 0 $\beta_{5,4}$ 0 $\alpha_{5}$ 0.78 $\beta_{1,5}$ 0 $\beta_{2,5}$ 0 $\beta_{3,5}$ 0 $\beta_{4,5}$ 0 $\beta_{5,5}$ 0 $\alpha_{6}$ 0.91 $\beta_{1,6}$ 0 $\beta_{2,6}$ 0 $\beta_{3,6}$ 0 $\beta_{4,6}$ 0 $\beta_{5,6}$ 0.4 $\alpha_{7}$ 0.98 $\beta_{1,7}$ 0 $\beta_{2,7}$ 0 $\beta_{3,7}$ 0 $\beta_{4,7}$ 0 $\beta_{5,7}$ 0.4 $\alpha_{8}$ 1.11 $\beta_{1,8}$ 0 $\beta_{2,8}$ 0 $\beta_{3,8}$ 0 $\beta_{4,8}$ 0 $\beta_{5,8}$ 0 $\alpha_{9}$ 1.21 $\beta_{1,9}$ 0 $\beta_{2,9}$ 0 $\beta_{3,9}$ 0 $\beta_{4,9}$ 0.4 $\beta_{5,9}$ 0 $\alpha_{10}$ 1.34 $\beta_{1,10}$ 0 $\beta_{2,10}$ 0 $\beta_{3,10}$ 0 $\beta_{4,10}$ 0 $\beta_{5,10}$ 0 $\beta_{6,1}$ 0 $\beta_{7,1}$ 0 $\beta_{8,1}$ 0 $\beta_{9,1}$ 0 $\beta_{10,1}$ 0 $\beta_{6,2}$ 0 $\beta_{7,2}$ 0.4 $\beta_{8,2}$ 0 $\beta_{9,2}$ 0 $\beta_{10,2}$ 0 $\beta_{6,3}$ 0 $\beta_{7,3}$ 0 $\beta_{8,3}$ 0 $\beta_{9,3}$ 0 $\beta_{10,3}$ 0 $\beta_{6,4}$ 0.4 $\beta_{7,4}$ 0 $\beta_{8,4}$ 0 $\beta_{9,4}$ 0 $\beta_{10,4}$ 0 $\beta_{6,5}$ 0.4 $\beta_{7,5}$ 0 $\beta_{8,5}$ 0 $\beta_{9,5}$ 0 $\beta_{10,5}$ 0 $\beta_{6,6}$ 0 $\beta_{7,6}$ 0 $\beta_{8,6}$ 0 $\beta_{9,6}$ 0 $\beta_{10,6}$ 0 $\beta_{6,7}$ 0 $\beta_{7,7}$ 0 $\beta_{8,7}$ 0.2 $\beta_{9,7}$ 0 $\beta_{10,7}$ 0 $\beta_{6,8}$ 0.4 $\beta_{7,8}$ 0.2 $\beta_{8,8}$ 0 $\beta_{9,8}$ 0 $\beta_{10,8}$ 0 $\beta_{6,9}$ 0 $\beta_{7,9}$ 0 $\beta_{8,9}$ 0 $\beta_{9,9}$ 0 $\beta_{10,9}$ 0.1 $\beta_{6,10}$ 0 $\beta_{7,10}$ 0 $\beta_{8,10}$ 0.4 $\beta_{9,10}$ 0.1 $\beta_{10,10}$ 0
• Table 2

Table 2Equilibrium values of $\textbf{\textit{Z}}^{\ast}$ of (17) for different values of $m_{k}$

 Parameter $\textit{m}_{k}=1$ $\textit{m}_{k}=2$ $\textit{m}_{k}=3$ $\textit{m}_{k}=4$ Parameter $\textit{m}_{k}=1$ $\textit{m}_{k}=2$ $\textit{m}_{k}=3$ $\textit{m}_{k}=4$ $\textit{x}^{\ast}_{1}$ 0.1755 0.0982 0.0680 0.0520 $\textit{u}^{\ast}_{1}$ 0.1595 0.1785 0.1854 0.1890 $\textit{x}^{\ast}_{2}$ 0.3199 0.1959 0.1401 0.1088 $\textit{u}^{\ast}_{2}$ 0.2666 0.3265 0.3503 0.3627 $\textit{x}^{\ast}_{3}$ 0.4110 0.2765 0.2066 0.1644 $\textit{u}^{\ast}_{3}$ 0.3161 0.4254 0.4769 0.5058 $\textit{x}^{\ast}_{4}$ 0.4691 0.3371 0.2618 0.2133 $\textit{u}^{\ast}_{4}$ 0.3351 0.4816 0.5609 0.6095 $\textit{x}^{\ast}_{5}$ 0.5045 0.3870 0.3124 0.2611 $\textit{u}^{\ast}_{5}$ 0.3363 0.5159 0.6248 0.6963 $\textit{x}^{\ast}_{6}$ 0.5560 0.4424 0.3660 0.3112 $\textit{u}^{\ast}_{6}$ 0.3475 0.5530 0.6862 0.7779 $\textit{x}^{\ast}_{7}$ 0.6302 0.5115 0.4293 0.3689 $\textit{u}^{\ast}_{7}$ 0.3707 0.6018 0.7575 0.8680 $\textit{x}^{\ast}_{8}$ 0.6496 0.5407 0.4628 0.4040 $\textit{u}^{\ast}_{8}$ 0.3609 0.6007 0.7713 0.8978 $\textit{x}^{\ast}_{9}$ 0.6949 0.5882 0.5101 0.4500 $\textit{u}^{\ast}_{9}$ 0.3657 0.6192 0.8054 0.9473 $\textit{x}^{\ast}_{10}$ 0.7136 0.6153 0.5413 0.4830 $\textit{u}^{\ast}_{10}$ 0.3568 0.6153 0.8119 0.9660

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