Shilnikov orbits in an autonomous third-order chaotic phase-locked loop

• Published in: IEEE transactions on circuits and systems. 1, Fundamental theory and applications Vol. 45; no. 9; pp. 979 - 983
• Main Authors: Watada, K., Endo, T., Seishi, H.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.09.1998; Institute of Electrical and Electronics Engineers
• Subjects: Applied sciences; Bifurcation; Chaos; Chaotic communication; Computer simulation; Electric, optical and optoelectronic circuits; Electronics; Equations; Exact sciences and technology; Filters; Orbital calculations; Orbits; Phase locked loops; Piecewise linear techniques; Theoretical study. Circuits analysis and design; Autonomous system; Carrier frequency; Computer simulation; Differential equation; Homoclinic orbit; Chaotic attractor; Non linear system; Phase locked loop; Piecewise linearization
• ISSN: 1057-7122; 1558-1268
• DOI: 10.1109/81.721264

In this work we investigate the Shilnikov homoclinic bifurcation in a new type of phase-locked loop (PLL) having a second-order loop filter. This system can be represented as a third-order autonomous system with piecewise-linear characteristics. By using piecewise-linear analysis, bifurcation equations for many types of homoclinic orbits are derived. Solving these equations gives many Shilnikov-type homoclinic orbits. We present bifurcation diagrams for the homoclinic orbits in the gain (K/sub 0/) versus detuning (/spl Delta//spl omega/) plane. Finally, we demonstrate the role of the homoclinic orbits in the global bifurcation of attractors both by computer simulation and experiments,.