We discuss the Giardinà-Kurchan-Peliti population dynamics method for evaluating large deviations of time-averaged quantities in Markov processes [Phys. Rev. Lett. 96, 120603 (2006)PRLTAO0031-900710.1103/PhysRevLett.96.120603]. This method exhibits systematic errors which can be large in some circumstances, particularly for systems with weak noise, with many degrees of freedom, or close to dyna...

A selective state observer capable of asymptotically tracking any arbitrarily chosen subset of the state vector of linear time-invariant multivariable dynamic systems is introduced. The dynamics of the observer are derived from a model of the subset to be estimated. It is shown that the only condition for the asymptotic tracking of the subset is that the derived model be observable. A simple an...

Two systematic methods are presented to guide the construction of Lyapunov functions for general infectious disease models and are thus applicable to establish their global dynamics. Specifically, a matrix-theoretic method using the Perron eigenvector is applied to prove the global stability of the disease-free equilibrium, while a graph-theoretic method based on Kirchhoff’s matrix tree theorem...

We present a computational method for finding attractors (ergodic sets of states) of Boolean networks under asynchronous update. The approach is based on a systematic removal of state transitions to render the state transition graph acyclic. In this reduced state transition graph, all attractors are fixed points that can be enumerated with little effort in most instances. This attractor set is ...

This paper gives a method to compute a controller that places closed-loop poles in a specified region, has an order equal to the number of plant control inputs and, under some assumptions, has prescribed controller dynamics. The proposed controller samples the plant outputs at a rate faster than the rate used for updating the control inputs; it is a multirate output controller or MROC. A system...

A time series analysis method for predicting the probability density of a dynamical system is proposed. A nonstationary parametric model of the probability density is estimated from data within a maximum likelihood framework and then extrapolated to forecast the future probability density and explore the system for critical transitions or tipping points. A full systematic account of parameter u...