2012/05/17 by Mozhgan Mombeini, Mombeini, Mozhgan, Ali Khaki Sedigh +3
Medicine · Physics and Astronomy · #Chaos control and synchronization #Chaotic Dynamics (nlin.CD) #Control #FOS: Physical sciences #I.2.7 #Mathematical and Theoretical Epidemiology and Ecology Models #Quantum chaos and dynamical systems #System Theory #nlin.CD
paper · pdf · doi:10.48550/arxiv.1205.3912
9 pages,Proceedings,Chaos 2011, 4th Chaotic Modeling and Simulation International Conference 31 May -- 3 June 2011, Agios Nikolaos, Crete Greece
arxiv created 2012/05/17 · openalex publication_date 2012/05/17 · arxiv updated 2012/05/18 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, a new approach to the problem of stabilizing a chaotic system is presented. In this regard, stabilization is done by sustaining chaotic properties of the system. Sustaining the chaotic properties has been mentioned to be of importance in some areas such as biological systems. The problem of stabilizing a chaotic singularly perturbed system will be addressed and a solution will be proposed based on the OGY (Ott, Grebogi and Yorke) methodology. For the OGY control, Poincare section of the system is defined on its slow manifold. The multi-time scale property of the singularly perturbed system is exploited to control the Poincare map with the slow scale time. Slow scale time is adaptively estimated using a parameter estimation technique. Control with slow time scale circumvents the need to observe the states. With this strategy, the system remains chaotic and chaos identification is possible with online calculation of lyapunov exponents. Using this strategy on ecological system improves their control in three aspects. First that for ecological systems sustaining the dynamical property is important to survival of them. Second it removes the necessity of insertion of control action in each sample time. And third it introduces the sufficient time for census.