Hidden attractors in dynamical models of phase-locked loop circuits : limitations of simulation in MATLAB and SPICE
Kuznetsov, N., Leonov, G. A., Yuldashev, M. V., & Yuldashev, R. V. (2017). Hidden attractors in dynamical models of phase-locked loop circuits : limitations of simulation in MATLAB and SPICE. Communications in Nonlinear Science and Numerical Simulation, 51, 39-49. doi:10.1016/j.cnsns.2017.03.010
© 2017 Elsevier B.V. This is a final draft version of an article whose final and definitive form has been published by Elsevier. Published in this repository with the kind permission of the publisher.
During recent years it has been shown that hidden oscillations, whose basin of attraction does not overlap with small neighborhoods of equilibria, may significantly complicate simulation of dynamical models, lead to unreliable results and wrong conclusions, and cause serious damage in drilling systems, aircrafts control systems, electromechanical systems, and other applications. This article provides a survey of various phase-locked loop based circuits (used in satellite navigation systems, optical, and digital communication), where such difficulties take place in MATLAB and SPICE. Considered examples can be used for testing other phase-locked loop based circuits and simulation tools, and motivate the development and application of rigorous analytical methods for the global analysis of phase-locked loop based circuits.