Chua’s oscillator: an introductory approach to chaos theory

Sordi, Alexandre

doi:10.1590/1806-9126-rbef-2020-0437

Cited by 3 publications

(1 citation statement)

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“…Chua created an electronic circuit with erratic behavior in or around 1983 [28]. Chua diodes, a type of nonlinear negative resistance, are used in this circuit [22].…”

Section: Modified Memristor Chua Circuitmentioning

confidence: 99%

Study of the dynamic properties of chaotic circuits in the presence of memristors

Kareem,

Husseini

2024

Preprint

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This paper first discusses a memristor model based on a multi-segment linear function with three different circuits. Then, based on the different values of the parameters of the memristors introduced, the dynamic behavior of these circuits is analyzed in terms of bifurcations, coexisting attractors, and complexity. Bifurcation analysis reveals the rich dynamic behavior of these circuits, including period-doubling bifurcations, bursts of chaos, and transients of chaos. The Muthuswamy exhibit dynamic phenomena including coexisting attractors, multistability, and super multistability under different initial conditions. Moreover, circuit simulation is used to confirm the existence and feasibility of the Chua circuit. Coexisting attractor’s generation circuits that can alter the initial values of arbitrary state variables are designed. The advantages of the proposed system are illustrated by comparisons with other chaotic attractors, which include controllable attracter number and direction, straightforward implementation circuits, and rich dynamic behavior. Lastly, the Colpitts circuit, which contains the BTJ transistor and becomes steadier when a memristor is substituted for it, as well as the coexistence of multiple chaotic attractors, end up being more stable. Simulation results indicate that the three proposed circuit schemes in this paper require less time to achieve complete dynamics than other circuit schemes. This feature improves the suggested circuit strategy's effectiveness and usability in practical applications.

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“…Chua created an electronic circuit with erratic behavior in or around 1983 [28]. Chua diodes, a type of nonlinear negative resistance, are used in this circuit [22].…”

Section: Modified Memristor Chua Circuitmentioning

confidence: 99%

Study of the dynamic properties of chaotic circuits in the presence of memristors

Kareem,

Husseini

2024

Preprint

View full text Add to dashboard Cite

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Extensive analysis for an innovative three-dimensional chaotic system with coexisting attractors

Jasim,

Alhasnawi,

Oglah

et al. 2024

Transport, Ecology, Sustainable Development: Eko Varna 2023

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A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

et al. 2021

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In this paper, a new fractional order chaotic system without equilibrium is proposed, analytically and numerically investigated, and numerically and experimentally tested. The analytical and numerical investigations were used to describe the system’s dynamical behaviors including the system equilibria, the chaotic attractors, the bifurcation diagrams, and the Lyapunov exponents. Based on the obtained dynamical behaviors, the system can excite hidden chaotic attractors since it has no equilibrium. Then, a synchronization mechanism based on the adaptive control theory was developed between two identical new systems (master and slave). The adaptive control laws are derived based on synchronization error dynamics of the state variables for the master and slave. Consequently, the update laws of the slave parameters are obtained, where the slave parameters are assumed to be uncertain and are estimated corresponding to the master parameters by the synchronization process. Furthermore, Arduino Due boards were used to implement the proposed system in order to demonstrate its practicality in real-world applications. The simulation experimental results were obtained by MATLAB and the Arduino Due boards, respectively, with a good consistency between the simulation results and the experimental results, indicating that the new fractional order chaotic system is capable of being employed in real-world applications.

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Chua’s oscillator: an introductory approach to chaos theory

Cited by 3 publications

References 0 publications

Study of the dynamic properties of chaotic circuits in the presence of memristors

Study of the dynamic properties of chaotic circuits in the presence of memristors

Extensive analysis for an innovative three-dimensional chaotic system with coexisting attractors

A New No Equilibrium Fractional Order Chaotic System, Dynamical Investigation, Synchronization, and Its Digital Implementation

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