Using thresholding at varying intervals to obtain different temporal patterns

Abstract

We show how stroboscopic threshold mechanisms can be effectively employed to obtain a wide range of stable cyclic behavior from chaotic systems, by simply varying the frequency of control. We demonstrate the success of the scheme in a prototypical one-dimensional map, as well as in a three-dimensional system modeling lasers where the threshold action is implemented on any one of the variables. It is evident that thresholding is capable of yielding exact limit cycles of varying periods and geometries when implemented at different intervals (even when very infrequent). This suggests a simple and potent mechanism for selecting different regular temporal patterns from chaotic dynamics.