A comparative study of two stochastic mode reduction methods

We present a comparative study of two methods for the reduction of the dimensionality of a system of ordinary differential equations that exhibits time-scale separation. Both methods lead to a reduced system of stochastic differential equations. The novel feature of these methods is that they allow the use, in the reduced system, of higher order terms in the resolved variables. The first method, proposed by Majda, Timofeyev and Vanden-Eijnden, is based on an asymptotic strategy developed by Kurtz. The second method is a short-memory approximation of the Mori-Zwanzig projection formalism of irreversible statistical mechanics, as proposed by Chorin, Hald and Kupferman. We present conditions under which the reduced models arising from the two methods should have similar predictive ability. We apply the two methods to test cases that satisfy these conditions. The form of the reduced models and the numerical simulations show that the two methods have similar predictive ability as expected.Comment: 35 pages, 6 figures. Under review in Physica

Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems

Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for phase-response curves, a fundamental one-dimensional phase reduction of oscillator models. The proposed theoretical and numerical analysis tools are illustrated on several system-theoretic questions and models arising in the biology of cellular rhythms

Application of parameter estimation to aircraft stability and control: The output-error approach

The practical application of parameter estimation methodology to the problem of estimating aircraft stability and control derivatives from flight test data is examined. The primary purpose of the document is to present a comprehensive and unified picture of the entire parameter estimation process and its integration into a flight test program. The document concentrates on the output-error method to provide a focus for detailed examination and to allow us to give specific examples of situations that have arisen. The document first derives the aircraft equations of motion in a form suitable for application to estimation of stability and control derivatives. It then discusses the issues that arise in adapting the equations to the limitations of analysis programs, using a specific program for an example. The roles and issues relating to mass distribution data, preflight predictions, maneuver design, flight scheduling, instrumentation sensors, data acquisition systems, and data processing are then addressed. Finally, the document discusses evaluation and the use of the analysis results