Dynamic processes on real-world networks are time-delayed due to finite processing speeds and the need to transmit data over nonzero distances. These time-delays often destabilize the network's dynamics, but are difficult to analyze because they increase the dimension of the network.We present results outlining an alternative means of analyzing these networks, by focusing analysis on the Lipschitz matrix of the relatively low-dimensional undelayed network. The key criteria, intrinsic stability, is computationally efficient to verify by use of the power method. We demonstrate applications from control theory and neural networks.
College and Department
Physical and Mathematical Sciences; Mathematics
BYU ScholarsArchive Citation
Reber, David Patrick, "Exponential Stability of Intrinsically Stable Dynamical Networks and Switched Networks with Time-Varying Time Delays" (2019). Theses and Dissertations. 7136.
time-varying time-delays, neural network, switched system