Generating chaotic attractors on a surface

Abstract: The present paper introduces a new method to generate several independent periodic attractors, based on a switching piecewise-constant controller. We demonstrate here that the state space equidistant repartition of these attractors is on an arbitrarily precise zone of a paraboloid or plane. We determine the state space domains where the attractors are generated from different initial conditions. A mathematical formula giving their maximal number in function of the controller piecewise-constant values is then deduced.

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