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Control of chaotic spatiotemporal spiking by time-delay autosynchronization
G Franceschini1, S Bose, E Schöll
1Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstrasse 36, D-10623 Berlin, Germany.
Summary
Global time-delayed feedback control stabilizes unstable periodic orbits in semiconductor charge transport. This method controls chaotic spatiotemporal patterns, enabling stabilization of different spatial patterns using feedback modification.
Area of Science:
- Condensed Matter Physics
- Nonlinear Dynamics
- Semiconductor Physics
Background:
- Reaction-diffusion systems model complex phenomena like charge transport.
- Bistable semiconductors exhibit chaotic behavior due to spatially extended dynamics.
- Unstable periodic orbits (UPOs) are crucial but difficult to control in chaotic systems.
Purpose of the Study:
- To apply global time-delayed feedback control to stabilize UPOs in a reaction-diffusion system for semiconductor charge transport.
- To investigate the effectiveness of an extended time-delay autosynchronization algorithm for controlling spatiotemporal chaos.
- To analyze the accuracy of control limits and explore pattern stabilization with spatial filtering.
Main Methods:
- Global time-delayed feedback control was implemented on a reaction-diffusion system.
- An extended time-delay autosynchronization algorithm was used to stabilize UPOs.
- Analytical approximations for control limits were evaluated and compared with simulation results.
- Spatial filtering was introduced into the feedback loop to modify control outcomes.
Main Results:
- The study successfully stabilized various spatiotemporal UPOs corresponding to spiking current filaments.
- High accuracy was achieved in extrapolating the required delay time for control.
- The theoretical limit for UPO control, based on the period and largest Lyapunov exponent, was not reached.
- Modifying the global feedback with a spatial filter allowed for the stabilization of distinct spatial patterns.
Conclusions:
- Global time-delayed feedback control is an effective method for stabilizing chaotic spatiotemporal dynamics in bistable semiconductor charge transport.
- The extended time-delay autosynchronization algorithm provides accurate control parameters, outperforming theoretical limits in practical application.
- Spatial filtering offers an additional mechanism to precisely control and stabilize desired spatial patterns within the system.