On complete chaotic maps with tent-map-like structures

Huang, Weihong

doi:10.1016/j.chaos.2004.09.021

Cited by 10 publications

(1 citation statement)

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“…The tent map structures have been observed in the transition of high-order band torus to high-order band chaos. Both characteristics have been referenced in chaos scenarios [Endler & Gallas, 2006;Huang, 2005] but, to our knowledge, they have not been reported in piecewise-smooth systems concerning nonsmooth torus destruction. This paper is organized as follows.…”

Section: Introductionmentioning

confidence: 96%

Bifurcation Analysis on Nonsmooth Torus Destruction Scenario of Delayed-PWM Switched Buck Converter

Taborda

Angulo

Olivar

2009

Int. J. Bifurcation Chaos

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In this paper, we propose a qualitative and quantitative dynamical study about the evolution of nonsmooth torus in a Digital Delayed Pulse-Width Modulator (PWM) switched buck converter. We explain the birth and destruction of the torus by successive discontinuity induced bifurcations (DIBs). The Digital-PWM control is based on Zero Average Dynamics (ZAD) strategy and a one-period delay is included in the control law. The control parameter (k s ) of the ZAD strategy can be varied in a large range, ideally (−∞, ∞). On these borders, the dynamical behavior is the same and thus an annulus-like parameter space is considered. Under variation of k s , the system gets closer to a codimension-two bifurcation point, where two simultaneous border-collision bifurcations (BC) meet. The system leaves the high-order periodic behavior and a high-order band torus appears. Wrinkles and nonsmoothness due to more and more successive bordercollisions bifurcations cause the torus destruction in high-order band chaos with tent-map-like structures and Mandelbrot-like sets. Finally, the chaotic bands merge in one-band chaos. The switched converter is modeled as a piecewise linear system where an analytical expression of the Poincaré map is available. Characteristics as duality, symmetry and recurrent behavior are determined using additional numerical methods for the Poincaré map decomposition in periodic sequences.

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Section: Introductionmentioning

confidence: 96%