Exploring the dynamics of a four-dimensional Chua-like system: Numerical simulations and hardware investigations

Vinicius F. R. Antunes, Cesar Manchein, Holokx A. Albuquerque, Luis Fernando Mello and Anderson Hoff
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Vinicius F. R. Antunes: Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville SC, Brazil
Cesar Manchein: Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville SC, Brazil
Holokx A. Albuquerque: Departamento de Física, Universidade do Estado de Santa Catarina, 89219-710 Joinville SC, Brazil
Luis Fernando Mello: Instituto de Matemática e Computação, Universidade Federal de Itajubá, 37500-903 Itajubá MG, Brazil
Anderson Hoff: Department of Chemistry, University of Calgary, 2500 University Drive N.W., Calgary, Alberta T2N 1N4, Canada

International Journal of Modern Physics C (IJMPC), 2025, vol. 36, issue 01, 1-22

Abstract: In this work, we employ simulations to investigate deterministic and stochastic dynamics of a system governed by four coupled nonlinear ordinary differential equations (ODEs) derived from the canonical three-dimensional Chua model, replacing the piecewise nonlinearity with a cubic function. We employed two simulation approaches: (i) using software — where we performed numerical simulations (digital computation) in the ODEs model, and (ii) using hardware — where we performed experimental studies (analog computation) in the ODEs model. In the initial software-based approach for simulations, we performed stability and bifurcation analyses of the trivial equilibrium point, which were analytically conducted, along with the numerical continuation method. We solved the model using digital computation and explored its intricate dynamical behavior through nonlinear dynamics techniques applied to the parameter planes. In the second approach, employing hardware for simulations through analog computation, we designed an electronic circuit using analog electronics to solve the model in a continuous-time integration. The experimental setup mirrored the numerical simulations, yielding comparable results in terms of dynamical behaviors. This study underscores significant agreement between numerical and experimental findings, highlighting the robustness of the model across digital and analog contexts and offering practical insights into the various nonlinear dynamics presented in this system.

Keywords: Chaos; simulation; analog computation; digital computation; Lyapunov exponent (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S0129183124501675

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