USING CHAOS TO KEEP PERIOD-MULTIPLIED SYSTEMS IN-PHASE

Periodically driven nonlinear systems can exhibit multiple-period beha vior (period-2, period-3, etc.). Several such systems, when driven wit h the same drive, can be on identical attractors but remain out of pha se with each other (e.g., one drive cycle for a period-doubled set of systems). This means that the basins of attraction for multiple-period systems can be divided into domains of attraction, one for each phase of the motion. A period-n attractor will have n domains of attraction in its basin. This out-of-phase situation is stable-small perturbatio ns will not succeed in getting the systems in phase. We show that one can often use an almost periodic driving signal (generated from variou s chaotic systems) which will simultaneously (1) keep the motion of th e systems nearly the same as the periodic driving case, (2) keep the b asin of attraction nearly the same, and (3) eliminate the n domains of attraction. In other words, there will be only one domain for the bas in. This means that any number of such driven systems will always be i n phase. We display this effect in simulations and actual electrical c ircuits, discuss the mechanism for this effect (which is most likely a crisis), and speculate on some applications of the technique.