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In this paper, a new approach to the problem of stabilizing a chaotic systemis presented. In this regard, stabilization is done by sustaining chaoticproperties of the system. Sustaining the chaotic properties has been mentionedto be of importance in some areas such as biological systems. The problem ofstabilizing a chaotic singularly perturbed system will be addressed and asolution will be proposed based on the OGY (Ott, Grebogi and Yorke)methodology. For the OGY control, Poincare section of the system is defined onits slow manifold. The multi-time scale property of the singularly perturbedsystem is exploited to control the Poincare map with the slow scale time. Slowscale time is adaptively estimated using a parameter estimation technique.Control with slow time scale circumvents the need to observe the states. Withthis strategy, the system remains chaotic and chaos identification is possiblewith online calculation of lyapunov exponents. Using this strategy onecological system improves their control in three aspects. First that forecological systems sustaining the dynamical property is important to survivalof them. Second it removes the necessity of insertion of control action in eachsample time. And third it introduces the sufficient time for census.

Adaptive control of the singularly perturbed chaotic systems based on the scale time estimation by keeping chaotic property