https://hal.inria.fr/hal-01790028Bagchi, SusmitSusmitBagchiGyeongsang National UniversityFormulating Analytical Solution of Network ODE Systems Based on Input ExcitationsHAL CCSD2018Computer Networks Convergent Functions Dynamic Networks Ordinary Differential EquationsConvergent FunctionsDynamic NetworksOrdinary Differential Equations[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM][INFO.INFO-LO] Computer Science [cs]/Logic in Computer Science [cs.LO][INFO.INFO-MO] Computer Science [cs]/Modeling and Simulation[INFO.INFO-SY] Computer Science [cs]/Systems and Control [cs.SY][MATH.MATH-CA] Mathematics [math]/Classical Analysis and ODEs [math.CA][INFO.INFO-DC] Computer Science [cs]/Distributed, Parallel, and Cluster Computing [cs.DC]Bagchi, Susmit2018-05-16 08:22:282022-07-28 17:20:192018-05-17 09:01:07enJournal articleshttps://hal.inria.fr/hal-01790028/document10.3745/JIPS.03.0092application/pdf1The concepts of graph theory are applied to model and analyze dynamics of computer networks, biochemicalnetworks and, semantics of social networks. The analysis of dynamics of complex networks is important inorder to determine the stability and performance of networked systems. The analysis of non-stationary andnonlinear complex networks requires the applications of ordinary differential equations (ODE). However, theprocess of resolving input excitation to the dynamic non-stationary networks is difficult without involvingexternal functions. This paper proposes an analytical formulation for generating solutions of nonlinearnetwork ODE systems with functional decomposition. Furthermore, the input excitations are analyticallyresolved in linearized dynamic networks. The stability condition of dynamic networks is determined. Theproposed analytical framework is generalized in nature and does not require any domain or range constraints.