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**Exponential stability of coupled systems on networks with mixed delays and reaction-diffusion terms.**
*(English)*
Zbl 1474.35369

Summary: This paper is concerned with the stability analysis issue for coupled systems on networks with mixed delays and reaction-diffusion terms (CSNMRs). By employing Lyapunov method and Kirchhoff’s Theorem in graph theory, a systematic method is proposed to guarantee exponential stability of CSNMRs. Two different kinds of sufficient criteria are derived in the form of Lyapunov function and coefficients of the system, respectively. Finally, a numerical example is given to show the effectiveness of the proposed criteria.

### MSC:

35K51 | Initial-boundary value problems for second-order parabolic systems |

35B35 | Stability in context of PDEs |

35K57 | Reaction-diffusion equations |

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\textit{W. Li} et al., Abstr. Appl. Anal. 2014, Article ID 780387, 9 p. (2014; Zbl 1474.35369)

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