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What is Flip Bifurcation

Chapter 11
Handbook of Research on Advanced Intelligent Control Engineering and Automation
A period doubling bifurcation in a discrete dynamical system. It is a bifurcation in which the system switches to a new behavior with twice the period of the original system. That is, there exists two points such that applying the dynamics to each of the points yields the other point. Such bifurcation occurs when the corresponding Floquet multiplier quits the unit circle at z =-1of the complex plain when it varies with respect to a given system parameter denoted as the bifurcation parameter.
Published in Chapter:
Bifurcation, Quasi-Periodicity, Chaos, and Co-Existence of Different Behaviors in the Controlled H-Bridge Inverter
Yosra Miladi (University of Sfax, Tunisia) and Moez Feki (University of Sfax, Tunisia)
Copyright: © 2015 |Pages: 32
DOI: 10.4018/978-1-4666-7248-2.ch011
Abstract
This chapter deals with the analysis of the dynamic behavior of a controlled single-phase H-bridge inverter. The authors show that in addition to border collision bifurcation, when it is controlled with a time-delayed controller or with a dynamic controller that increases the system dimension, the H-bridge inverter can exhibit several other types of behaviors such as Neimark-Sacker bifurcation, quasi-periodicity, and coexistence of different periodic behaviors, as well as coexistence between periodic and chaotic behaviors. The proposed controllers are of different types. In addition to the Fixed-Point Induced Controller (FPIC), the authors also present the Time-Delayed Feedback Controller (TDFC) and the dynamic linear controller, such as the proportional-integral controller. The main issue of this chapter is to perform analysis within and beyond the stability region. Analytic calculation and numerical simulations are presented to confirm the obtained results.
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Chapter 111
Logistic Models for Symbiosis, Predator-Prey, and Competition
Also known as period-doubling bifurcation. The physical trace of this bifurcation is the period doubling (or frequency halving) of the periodic time signal generated by the system.
Published in Chapter: Logistic Models for Symbiosis, Predator-Prey, and Competition; From: Encyclopedia of Networked and Virtual Organizations
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