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Hidden attractors in dynamical models of phase-locked loop circuits: Limitations of simulation in MATLAB and SPICE

Nikolay Kuznetsov, +5 more
- 01 Oct 2017 - 
- Vol. 51, pp 39-49
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TLDR
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.
About: 
This article is published in Communications in Nonlinear Science and Numerical Simulation.The article was published on 2017-10-01 and is currently open access. It has received 140 citations till now. The article focuses on the topics: Phase-locked loop.

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Citations
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Journal ArticleDOI

Initial condition-dependent dynamics and transient period in memristor-based hypogenetic jerk system with four line equilibria

Han Bao, +5 more
- 01 Apr 2018 - 
TL;DR: By introducing an ideal and active flux-controlled memristor into an existing hypogenetic chaotic jerk system, an interesting Memristor-based chaotic system with hypogenetics jerk equation and circuit forms is proposed, which exhibits the extreme multistability phenomenon of coexisting infinitely many attractors.
Journal ArticleDOI

Coexisting Behaviors of Asymmetric Attractors in Hyperbolic-Type Memristor based Hopfield Neural Network.

Bocheng Bao, +5 more
- 23 Aug 2017 - 
TL;DR: It is numerically shown that the memristive HNN has a dynamical transition from chaotic, to periodic, and further to stable point behaviors with the variations of the Memristor inner parameter, implying the stabilization effect of the hyperbolic-type memristor on the chaotic HNN.
Journal ArticleDOI

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

Nikolay Kuznetsov, +5 more
- 31 Jan 2018 - 
TL;DR: In this article, the Rabinovich system can exhibit a hidden attractor in the case of multistability as well as a classical self-excited attractor, and the concept of finite-time Lyapunov dimension is developed for numerical study of the dimension of attractors.
Journal ArticleDOI

Generating one to four-wing hidden attractors in a novel 4D no-equilibrium chaotic system with extreme multistability

Sen Zhang, +4 more
- 12 Jan 2018 - 
TL;DR: By using a simple state feedback controller in a three-dimensional chaotic system, a novel 4D chaotic system is derived and the unusual and striking dynamic behavior of the coexistence of infinitely many hidden attractors is revealed by selecting the different initial values of the system, which means that extreme multistability arises.
Journal ArticleDOI

Numerical analyses and experimental validations of coexisting multiple attractors in Hopfield neural network

Bocheng Bao, +6 more
- 22 Sep 2017 - 
TL;DR: By simplifying connection topology of Hopfield neural network with three neurons, a kind of HNN-based nonlinear system is proposed and dynamical behaviors with the variation of the adjusting parameter are discussed and coexisting multiple attractors’ behavior under different state initial values are investigated.
References
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Book

Phaselock Techniques

F. M. Gardner
TL;DR: This book represents the second edition of Gardner's widely known book on phaselock principles and applications, and Gardner has clearly written for the practitioner, providing the necessary information with a minimum of rigor and a succinct writing style.
Book

Phase-locked loops : design, simulation, and applications

Roland E. Best
TL;DR: This chapter discusses the design procedure for Mixed-Signal PLLs, and the PLL in Communications, and discusses the Pull-in Process and the Laplace Transform.
Book

Principles of coherent communication

Andrew J. Viterbi
Journal ArticleDOI

Hidden Attractors in Dynamical Systems. From Hidden Oscillations in Hilbert-Kolmogorov Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits

Gennady A. Leonov, +2 more
- 05 Mar 2013 - 
TL;DR: The problem of investigating hidden oscillations arose in the second part of Hilbert's 16th problem (1900), and the first nontrivial results were obtained in Bautin's works, which revealed no similar transient processes leading to such attractors.
Journal ArticleDOI

Localization of hidden Chuaʼs attractors

Gennady A. Leonov, +3 more
- 06 Jun 2011 - 
TL;DR: In this article, the authors proposed to use a special analytical-numerical algorithm to locate hidden attractors of Chua's circuit. But this algorithm does not consider the hidden attractor of the neighborhood of equilibrium.
Related Papers (5)

Hidden Attractors in Dynamical Systems. From Hidden Oscillations in Hilbert-Kolmogorov Aizerman, and Kalman Problems to Hidden Chaotic Attractor in Chua Circuits

Gennady A. Leonov, +2 more
- 05 Mar 2013 - 

Homoclinic orbits, and self-excited and hidden attractors in a Lorenz-like system describing convective fluid motion

Gennady A. Leonov, +4 more
- 27 Jul 2015 - 

Determining Lyapunov exponents from a time series

A. Wolf, +3 more
- 01 Jul 1985 - 

Localization of hidden Chuaʼs attractors

Gennady A. Leonov, +3 more
- 06 Jun 2011 - 

Hidden attractors in dynamical systems

Dawid Dudkowski, +6 more
- 03 Jun 2016 - 
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Q1. What are the contributions in "Hidden attractors in dynamical models of phase-locked loop circuits: limitations of simulation in matlab and spice" ?

In this article 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, is provided.