skip to main content

Title: Reliability of unstable periodic orbit based control strategies in biological systems

Presence of recurrent and statistically significant unstable periodic orbits (UPOs) in time series obtained from biological systems is now routinely used as evidence for low dimensional chaos. Extracting accurate dynamical information from the detected UPO trajectories is vital for successful control strategies that either aim to stabilize the system near the fixed point or steer the system away from the periodic orbits. A hybrid UPO detection method from return maps that combines topological recurrence criterion, matrix fit algorithm, and stringent criterion for fixed point location gives accurate and statistically significant UPOs even in the presence of significant noise. Geometry of the return map, frequency of UPOs visiting the same trajectory, length of the data set, strength of the noise, and degree of nonstationarity affect the efficacy of the proposed method. Results suggest that establishing determinism from unambiguous UPO detection is often possible in short data sets with significant noise, but derived dynamical properties are rarely accurate and adequate for controlling the dynamics around these UPOs. A repeat chaos control experiment on epileptic hippocampal slices through more stringent control strategy and adaptive UPO tracking is reinterpreted in this context through simulation of similar control experiments on an analogous but stochastic computermore » model of epileptic brain slices. Reproduction of equivalent results suggests that far more stringent criteria are needed for linking apparent success of control in such experiments with possible determinism in the underlying dynamics.« less
Authors:
;  [1] ;  [2] ;  [3] ;  [4]
  1. Department of Physics and Astrophysics, University of Delhi, Delhi 110007 (India)
  2. Institut für Höchstleistungsrechnen, Universität Stuttgart, D-70569 Stuttgart (Germany)
  3. Cluster Innovation Center, University of Delhi, Delhi 110007 (India)
  4. (India)
Publication Date:
OSTI Identifier:
22402548
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ALGORITHMS; BRAIN; CHAOS THEORY; COMPUTERIZED SIMULATION; CONTROL; DETECTION; DYNAMICS; NOISE; ORBITS; PERIODICITY; STATISTICS; STOCHASTIC PROCESSES