2018/01/10 by Fadi Antown, Davor Dragičević, Gary Froyland · 18 citations
Business, Management and Accounting · Mathematics · Physics and Astronomy · #Advanced Queuing Theory Analysis #Dynamical systems theory #Linear dynamical system #Linear system #Markov Chains and Monte Carlo Methods #Markov chain #Markov process #Perturbation (astronomy) #Projected dynamical system #Stationary distribution #Transfer operator #math.DS #stochastic dynamics and bifurcation
paper · pdf · doi:10.1007/s10955-018-1985-1
published in Journal of Statistical Physics 170(6), 1051-1087 (Springer Science+Business Media)
arxiv created 2018/01/10 · openalex created_date 2018/01/26 · openalex publication_date 2018/02/19 · arxiv updated 2018/04/04 · openalex updated_date 2026/08/05
The linear response of a dynamical system refers to changes to properties of the system when small external perturbations are applied. We consider the little-studied question of selecting an optimal perturbation so as to (i) maximise the linear response of the equilibrium distribution of the system, (ii) maximise the linear response of the expectation of a specified observable, and (iii) maximise the linear response of the rate of convergence of the system to the equilibrium distribution. We also consider the inhomogeneous or time-dependent situation where the governing dynamics is not stationary and one wishes to select a sequence of small perturbations so as to maximise the overall linear response at some terminal time. We develop the theory for finite-state Markov chains, provide explicit solutions for some illustrative examples, and numerically apply our theory to stochastically perturbed dynamical systems, where the Markov chain is replaced by a matrix representation of an approximate annealed transfer operator for the random dynamical system.