Abstract. The goal of this paper is to study the stabilization of chaos in dynamical systems by adding nonlinear feedback. We analyze what happens when two control parameters, the gain and the parameter memory, are considered. It is shown that the introduction of the additional control of the memory parameter does not extend the class of admissible maps. It appears, however, that a stabilizing control may use a variety of time shifts. In this case, one can change the nature of the decay of a chaotic regime, making it smoother, which may be of significance in the management of biological, economical and medical systems.

DOI: 10.14232/actasm-014-522-z

AMS Subject Classification (1991): 42A05, 39A30

Keyword(s): trigonometric polynomials, dynamical systems, optimal control of chaos

Received March 26, 2014, and in revised form August 15, 2016. (Registered under 22/2014.)