Robust chaos-the theoretical formulation and experimental evidence

Banerjee, Soumitro; Kastha, Debaprasad; Das, S.; Vivek, G.; Grebogi, Celso

doi:10.1109/iscas.1999.777567

Cited by 9 publications

(11 citation statements)

References 5 publications

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“…Power converters [40,77] exhibit several nonlinear phenomena such as border-collision bifurcations, coexisting attractors (alternative stable operating modes or fragile chaos), and chaos (apparently random behavior). These phenomena are created by switching elements [40].…”

Section: Robust Chaos In 2-d Piecewise Smooth Mapsmentioning

confidence: 99%

“…Now it is shown in Refs. [13,77] that the resulting chaos from the 2-D map (7) is robust in the following cases:…”

Section: Robust Chaos In 2-d Piecewise Smooth Mapsmentioning

confidence: 99%

“…This method was used essentially (with other techniques) for both 2-D piecewise smooth maps [11,13,47,69,77] and 3-D continuous-time systems [18]. In both cases, the robustness was proved analytically and confirmed numerically, and in some cases the results were confirmed experimentally.…”

Section: Normal Form Analysismentioning

confidence: 99%

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On the robustness of chaos in dynamical systems: Theories and applications

Elhadj

Sprott

2008

Front. Phys. China

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This paper offers an overview of some important issues concerning the robustness of chaos in dynamical systems and their applications to the real world. PACS numbers 05.45.-a, 05.45.GgChaotic dynamical systems display two kinds of chaotic attractors: One type has fragile chaos (the attractors disappear with perturbations of a parameter or coexist with other attractors), and the other type has robust chaos, defined by the absence of periodic windows and coexisting attractors in some neighborhood of the parameter space. The existence of these windows in some chaotic regions means that small changes of the parameters would destroy the chaos, implying the fragility of this type of chaos.Contrary to this situation, there are many practical applications, such as in communication and spreading the spectrum of switch-mode power supplies to avoid electromagnetic interference [15, 16], where it is necessary to obtain reliable operation in the chaotic mode, and

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Section: Robust Chaos In 2-d Piecewise Smooth Mapsmentioning

confidence: 99%

“…Now it is shown in Refs. [13,77] that the resulting chaos from the 2-D map (7) is robust in the following cases:…”

Section: Robust Chaos In 2-d Piecewise Smooth Mapsmentioning

confidence: 99%

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On the robustness of chaos in dynamical systems: Theories and applications

Elhadj

Sprott

2008

Front. Phys. China

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“…Actually, it was shown in [9] that most controlled DC-DC converters like the voltage-mode controlled buck converter can be represented by piecewise smooth maps and such type of maps generates robust chaos, defined by the absence of periodic windows and coexisting attractors in some neighborhood of parameter space.…”

Section: Simulation Results and Commentsmentioning

confidence: 99%

Chaotic Behavior in a Switched Dynamical System

Guezar

Bouzahir

2008

Modelling and Simulation in Engineering

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We present a numerical study of an example of piecewise linear systems that constitute a class of hybrid systems. Precisely, we study the chaotic dynamics of the voltage-mode controlled buck converter circuit in an open loop. By considering the voltage input as a bifurcation parameter, we observe that the obtained simulations show that the buck converter is prone to have subharmonic behavior and chaos. We also present the corresponding bifurcation diagram. Our modeling techniques are based on the new French native modeler and simulator for hybrid systems called Scicos (Scilab connected object simulator) which is a Scilab (scientific laboratory) package. The followed approach takes into account the hybrid nature of the circuit.

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“…However, there are certain guidelines to follow when purposely using the chaotic properties of a converter. In [29], the authors have identified the regions of operation to ensure reliable chaotic operation (robust chaos) and a boost topology was tested satisfactorily.…”

Section: Future Workmentioning

confidence: 99%

Development of tools for the study of chaotic behavior in power electronics

Colón

Contreras

Rodrı́guez

et al.

COMPEL 2000. 7th Workshop on Computers in Power Electronics. Proceedings (Cat. No.00TH8535)

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Abstraa -This paper describes the development of software tools for the analysis of chaos in power electronics systems. This project was motivated by potential contributions of chaos theory in the design, analysis and control of power electronics circuits. Nonlinear analysis software and computer programs were used for the detection and analysis of chaotic components. Simulations of power electronics &-vices were performed using commercially available circuit analysis packages. The voltage and current time series obtained from the circuit analysis were studied using the nonlinear analysis tools developed for this project as well as existing nonlinear analysis programs. The results of the nonlinear analysis can be used to design and implement better mitigating and control techniques for the circuits under study. Chaotic dynamics provide an alternate representation that can lead to better designs and new ways to explain nonlinear behavior in power electronics circuits. There is also a great pedagogical value in complementing the traditional representation of power electronic circuits with alternate models.

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Robust chaos-the theoretical formulation and experimental evidence

Cited by 9 publications

References 5 publications

On the robustness of chaos in dynamical systems: Theories and applications

On the robustness of chaos in dynamical systems: Theories and applications

Chaotic Behavior in a Switched Dynamical System

Development of tools for the study of chaotic behavior in power electronics

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