Formulating Analytical Solution of Network ODE Systems Based on Input Excitations
Abstract
The concepts of graph theory are applied to model and analyze dynamics of computer networks, biochemical
networks and, semantics of social networks. The analysis of dynamics of complex networks is important in
order to determine the stability and performance of networked systems. The analysis of non-stationary and
nonlinear complex networks requires the applications of ordinary differential equations (ODE). However, the
process of resolving input excitation to the dynamic non-stationary networks is difficult without involving
external functions. This paper proposes an analytical formulation for generating solutions of nonlinear
network ODE systems with functional decomposition. Furthermore, the input excitations are analytically
resolved in linearized dynamic networks. The stability condition of dynamic networks is determined. The
proposed analytical framework is generalized in nature and does not require any domain or range constraints.
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