International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/2363 2020 2020 Directorate of Education of Babylon, Ministry of Education, Babylon, Iraq Raad Safah A. AL†.. Department of Software, Information Technology, University of Babylon, Babylon, Iraq Hayder Kadhim .. Mathematics Department, University of Babylon, Hilla, Babylon, Iraq May A. Abdul-Khaled AL AL-Yaseen We investigate the stability of huge, linked subsystems in separate nonlinear dynamical systems. These systems' properties depend on both their dynamics and their link structure. We examine two concepts of stability. The initial one is connection stability, where a complete system is robust in the meaning of Lyapunov given the uncertainty and temporal fluctuations in the linking lengths among systems. The next is the widely accepted idea of asymptotic stability of the entire system, which is predicated on the premise that all linkages are set at the nominal values. We propose graph-based characteristics of two types of a stable for the situation of homogenous subsystems by making linkages to spectrum graph theory, in particular the spectrum of the sign adjacency matrix. We also obtain constraints on the highest amplitude of the sign adjacency matrix of independent relevance via this method. 2024 2024 129 155 10.54216/IJNS.230212 https://www.americaspg.com/articleinfo/21/show/2363