Most approaches to the analysis of autonomous nonlinear networks fall under one or more of three categories: topological techniques, stability analysis, and approximate methods. The first method is universal, linear or nonlinear. The application of computer techniques has given strong emphasis to the latter. Approximate methods can give results on estimations of how network components affect stability.
This paper is an investigation of the stability of nonlinear resistance in autonomous dynamic networks through approximate methods.
A system that is both unforced and time-invariant is called autonomous. Linear autonomous networks lend themselves to general analytic solutions. With nonlinear autonomous networks, however, such is not the case. In dealing with nonlinear networks, we are constantly concerned with the equilibrium state. This is a point in the state space where the network has a constant solution at this point. Under certain conditions, the state, when perturbed from its equilibrium point, will return or stay near its equilibrium point.
A Taylor Series expansion of the state of a nonlinear autonomous network about its equilibrium state yields a linearized model which, in many cases, approximates quite closely the nonlinear network in some nhd of the equilibrium point. This approximation can provide qualitative criteria in establishing the operating properties of the nonlinear autonomous network. If the nonlinear network is stable, it is useful to know if the system is asymptotically stable and in what nhd (neighborhood). That is, we ask "does the perturbed state approach its equilibrium point with the passage of time and over what region?" A nonlinear network that has only one asymptotically stable equilibrium state is called globally asymptotically stable.
Level of Degree
Electrical and Computer Engineering
First Committee Member (Chair)
Second Committee Member
Third Committee Member
Bornholdt, John Jerome. "A Numerical Investigation Of Nonlinear Resistance In Second-Order Autonomous Dynamic Networks." (1979). https://digitalrepository.unm.edu/ece_etds/540