Stabilizing long-period orbits via symbolic dynamics in simple limiter controllers

Abstract

We present an efficient approach to determine the control parameter of simple limiter controllers by using symbolic dynamics of one-dimensional unimodal maps. By applying addition- and subtraction-symbol rules for generating an admissible periodic sequence, we deal with the smallest base problem of the digital tent map. The proposed solution is useful for minimizing the configuration of digital circuit designs for a given target sequence. With the use of the limiter controller, we show that one-dimensional unimodal maps may be robustly employed to generate the maximum-length shift-register sequences. For an arbitrary long Sarkovskii sequence, the control parameters are analytically given.

Stabilizing biological populations and metapopulations through Adaptive Limiter Control

“…This adaptive nature of the algorithm makes it 14 independent of the range of the size of the populations to be controlled, thus enhancing its 15 applicability. ALC belongs to the so called "limiter control" family of algorithms (Corron et al, 16 2000;Hilker and Westerhoff, 2006;Zhou, 2006), although to the best of our knowledge, this 17 particular scheme has not been proposed earlier in any context. 18 19 We began with an investigation of the effects of ALC on the steady-state behaviour of a 20 simple one-dimensional population dynamics model.…”