Deterministic uncertainty
Bartosz Telenczuk, Miroslaw Latka, Bruce J. West
Abstract
Equations of motion with delays naturally emerge in the analysis of complex biological control systems which are organized around biochemically mediated feedback interactions. We study the properties of a Mackey-Glass-type nonlinear map with delay -- the deterministic part of the stochastic cerebral blood flow map (CBFM) recently introduced to elucidate the scaling properties of cerebral hemodynamics. We point out the existence of deterministic and nondeterministic subspaces in the reconstructed phase space of delay-difference equations and discuss the problem of detection of nonlinearities in time series generated by such dynamical systems.
Create a lesson
Related papers
PRISM: Unifying multiphysics optothermal transport and identifiability-guided inference for nanoscale thermal metrology
Yicong Qiu, Ziyang Zhong, Ziyan Qian et al.
Ultraslow diffusion emerging from local symmetry breaking in quenched disorder
Jin Liu, Rainer Klages, Huihai Wang et al.
A model for the dimension of the inertial manifold of the Kuramoto-Sivashinsky equation
Melisa Y. Vinograd, Patricio Clark di Leoni
When chaos meets thermodynamics: from Fermi acceleration to thermalisation
Edson Denis Leonel
Three-Wave Forced Hasegawa--Wakatani Model: Reducing Chaos with Zonal Flows
P. Haerter, R. L. Viana, I. L. Caldas
Flatness-based control of nonlinear complex networks
I. Sendiña-Nadal, I. Leyva, J. P. Barbot et al.