Stability analysis of a class of electronic circuits based on thermodynamic principles part II: analysis of chaos in Chua’s circuit

In this paper, the generation of n × m-scroll attractors under a Chua-circuit framework is presented. By using a sawtooth function, f1(x), and a staircase function, f2(y), n × m-scroll attractors can be generated and observed from a third-order circuit. Its dynamical behaviors are investigated by means of theoretical analysis as well as numerical simulation. Moreover, two electronic circuits are designed for its realization, and experimental observations of n × m-scroll attractors based on Chua's circuit are reported, for the first time in the literature.

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Fixed Point Stability Analysis of Chua's Circuit: A Case Study with a Real Circuit

Journal of Circuits System and Computers ◽

10.1142/s0218126697000085 ◽

1997 ◽

Vol 07 (02) ◽

pp. 111-115 ◽

Cited By ~ 2

Author(s):

Luis A. Aguirre ◽

Leonardo A. B. Tôrres

Keyword(s):

Fixed Point ◽

Stability Analysis ◽

Internal Resistance ◽

Short Paper ◽

Chua’S Circuit ◽

Chaotic Oscillations ◽

Chua's Circuit

This short paper discusses the effect of the internal resistance of the inductor in Chua's circuit which is often neglected by many even when actual implementation is intended. Using a fixed point stability analysis it is shown that varying the inductor resistance it is possible to suppress or allow chaotic oscillations. The results reported in this paper have clear consequences for the control of Chua's circuit.

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Stability Analysis of Fourth-Order Chua’s Circuit

Advances in Neural Networks – ISNN 2011 - Lecture Notes in Computer Science ◽

10.1007/978-3-642-21105-8_29 ◽

2011 ◽

pp. 241-250

Author(s):

Chunfang Miao ◽

Yunquan Ke

Keyword(s):

Stability Analysis ◽

Fourth Order ◽

Chua’S Circuit ◽

Chua's Circuit

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Stability Analysis and Mapping of Multiple Dynamics of Chua’s Circuit in Full Four-Parameter Spaces

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127415300372 ◽

2015 ◽

Vol 25 (13) ◽

pp. 1530037 ◽

Cited By ~ 8

Author(s):

Ronilson Rocha ◽

Rene Orlando Medrano-T.

Keyword(s):

Stability Analysis ◽

Theoretical Analysis ◽

Initial Conditions ◽

Equilibrium Points ◽

Chua’S Circuit ◽

Parameter Spaces ◽

Chua's Circuit ◽

Describing Functions ◽

Route To Chaos ◽

The Stability

The stability analysis is used in order to identify and to map different dynamics of Chua’s circuit in full four-parameter spaces. The study is performed using describing functions that allow to identify fixed point, periodic orbit, and unstable states with relative accuracy, as well as to predict route to chaos and hidden dynamics that conventional computational methods do not detect. Numerical investigations based on the computation of eigenvalues and Lyapunov exponents partially support the predictions obtained from the theoretical analysis since they do not capture the multiple dynamics that can coexist in the operation of Chua’s circuit. Attractors obtained from initial conditions outside of neighborhoods of the equilibrium points confirm the multiplicity of dynamics in the operation of Chua’s circuit and corroborate the theoretical analysis.

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Discontinuous Control and Stability Analysis of Step-Down DC-DC Voltage Converters

Engineering and Technology Journal ◽

10.30684/etj.v38i3a.567 ◽

2020 ◽

Vol 38 (3A) ◽

pp. 446-456

Author(s):

Bashar F. Midhat

Keyword(s):

Stability Analysis ◽

Lyapunov Stability ◽

Control Method ◽

Power Electronic ◽

Electronic Circuits ◽

Dc Voltage ◽

Power Electronic Circuits ◽

Lyapunov Stability Criterion ◽

Control Step ◽

Step Down

Step down DC-DC converters are power electronic circuits, which mainly used to convert voltage from a level to a lower level. In this paper, a discontinuous controller is proposed as a control method in order to control Step-Down DC-DC converters. A Lyapunov stability criterion is used to mathematically prove the ability of the proposed controller to give the desired voltage. Simulationsl1 are performedl1 in MATLABl1 software. The simulationl1 resultsl1 are presentedl1 for changesl1 in referencel1 voltagel1 and inputl1 voltagel1 as well as stepl1 loadl1 variations. The resultsl1 showl1 the goodl1 performancel1 of the proposedl1 discontinuousl1 controller.

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