Chaos and bifurcation in a third-order phase locked loop. (English) Zbl 1085.93514
Summary: The chaos induced in a new type of phase locked loop (PLL) having a second-order loop filter is investigated. The system under consideration is modeled as a third-order autonomous system with sinusoidal phase detector characteristics. The modern results of nonlinear theory, such as bifurcation and chaos, are applied to a third-order PLL. A method is developed to quantitatively study the type of bifurcations that occur in this type of PLLs. The study shows that PLL experiences a Hopf bifurcation point as well as chaotic behaviour. The method of multiple scales is used to find the normal form near the Hopf bifurcation point. The point is found to be a supercritical one.
MSC:
| 93C40 | Adaptive control/observation systems |
| 37G40 | Dynamical aspects of symmetries, equivariant bifurcation theory |
| 37G05 | Normal forms for dynamical systems |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 37D45 | Strange attractors, chaotic dynamics of systems with hyperbolic behavior |
| 93E11 | Filtering in stochastic control theory |
Keywords:
second-order loop filter; third-order autonomous system; Hopf bifurcation; chaotic behaviour; method of multiple scales; normal formReferences:
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