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.

No abstract

No abstract

The attractors of the equation describing a phase locked loop (PLL) injected with a periodic external force may have both (chaotic) attractors of the first kind bifurcated from a stable spiral vortex and those (chaos) bifurcated from the limit cycle of the second kind circulating around the cylindrical coordinate system. It is known that there exists a chaotic attractor in the form of these two types fused together. In the present study, the region of existence is studied for these (chaotic) attractors in the PLL equation. It is made clear that the extinction mechanism for these attractors is mainly due to the Heteroclinic Tangency Crisis caused by transitional chaining of the α and ω branches of the inverse unstable invariant point (I) and the definite unstable invariant point (D). Further, this paper investigates Crisis‐Induced Intermittency, which is seen when chaotic attractors of the first and second kinds are fused due to explosion of the chaotic attractor of either the first or the second kind. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 84(3): 52–61, 2001

No abstract