Periodic Forcing and Goal Oriented Control of Chaos

Abstract

We study control of chaos by periodic modulation without feedback in discrete maps. We show that period-p forcing shifts and splits the naturally occurring period-p windows (and their multiples) and leads to the stabilization of chaos, and that for multiplicative sinusoidal perturbations of the logistic map stabilization can be done at a desired value of the control parameter and at a desired periodicity, simply by varying the amplitude of forcing, provided the modulated system remains bounded.

Period adding bifurcation in a logistic map with memory

“…where r 0 + g n is never greater than four and g n can have various complicated forms but it has always been local [14][15][16][17][18][19][20]. Our departure from the usual practice is that our g n is memory dependent [13].…”