Iterations of perturbed tent maps with applications to chaos control

B. T. Polyak, E. N. Gryazina

Результат исследований: Глава в книге, отчете, сборнике статейМатериалы для конференциирецензирование

1 Цитирования (Scopus)


Iterations of 1D simple maps such as logistic, tent, cubic ones are very well studied. However perturbed versions of these maps (close in uniform norm but with strongly varying derivatives) can exhibit completely different behavior. We encounter such situation when dealing with chaos stabilization via small control. In this paper we present analytical investigation of this effect for one particular case - piecewise linear perturbation of the tent map. Surprisingly, iterations of this map converge to the unique fixed point very fast for all initial points. The result is in sharp contrast with iterations of the original tent map but explains fast stabilization of unstable periodic orbits by predictive control, proposed in Polyak & Maslov (2005); Polyak (2005).

Язык оригиналаАнглийский
Название основной публикации1st IFAC Conference on Analysis and Control of Chaotic Systems, CHAOS'06
ИздательIFAC Secretariat
Число страниц5
ИзданиеPART 1
ISBN (печатное издание)9783902661098
СостояниеОпубликовано - 2006
Опубликовано для внешнего пользованияДа

Серия публикаций

НазваниеIFAC Proceedings Volumes (IFAC-PapersOnline)
НомерPART 1
ISSN (печатное издание)1474-6670


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