A time delay in the response of the neurons in a network can induce sustained oscillation and chaos. We present a stability criterion based on local stability analysis to prevent sustained oscillation in symmetric delay networks, and show an example of chaotic dynamics in a non-symmetric delay network.

The paper suggests conditions for presence of quadratic Lyapunov functions for nonlinear observer based feedback systems with an ’input nonlinearity’ in the feedback path. Provided that the system using state feedback satisfies the circle criterion (i.e., when all states can be measured), we show that stability of the extended system with output feedback control from a (full state) Luenberger-t...

We consider a class of systems with a cyclic interconnection structure that arises, among other examples, in dynamic models for certain biochemical reactions. We first show that a “secant” criterion for local stability, derived earlier in the literature, is in fact a necessary and sufficient condition for diagonal stability of the corresponding class of matrices. We then revisit a recent genera...

This paper addresses closed-loop stability analysis of PID controlled local model networks. The proposed method allows to investigate exponential or asymptotic stability of the closed-loop system. For this purpose a common quadratic Lyapunov function is used as stability criterion. Due to the fact that the Lyapunov approach requires a state-space model a suitable closed-loop state-space system ...

We prove a criterion for the global stability of the positive equilibrium in discrete-time single-species population models of the form xn+1 = xnF (xn). This allows us to demonstrate analytically (and easily) the conjecture that local stability implies global stability in some well-known models, including the Ricker difference equation and a combination of the models by Hassel and Maynard Smith...