EXPLOSION OF STRANGE ATTRACTORS AND CRISIS-INDUCED INTERMITTENCY FROM A FORCED PHASE-LOCKED LOOP CIRCUIT: THEORY AND EXPERIMENTS

Abstract

In this article, we investigate a mechanism of explosion and extinction of strange attractors and their crisis-induced intermittency observed after the explosion in the PLL equation used as an FM-demodulator. Namely, we elucidate that, explosion of the first type P1 (second type P2) chaotic attractor to their marged P1&P2-chaotic attractor occurs due to the heteroclinic tangency between an unstable manifold of the inversely unstable fixed point, and a stable manifold of the associated directly unstable fixed point (I-D chain). We demonstrate this explosion both by computer simulation and electronic circuit experiments.