Connectivity estimations of errors of linearization of essentially nonlinear systems

We consider a nonlinear dynamical system with several connectivity components. It includes subsystems which can be switched off or on in the operation process, i.e., the system undergoes structural changes. It is well-known that such systems are stable with respect to the connectivity. This property is known as the connectivity stability. In this paper we find an upper bound for the solution of the initial multiply-connected domain of a nonlinear dynamical system and obtain a connectivity estimation for its linearization error.