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<p>This paper presents a novel 4D chaotic system characterized by the incorporation of a tangent hyperbolic memristor, which introduces additional nonlinearity into its dynamic framework. The system exhibits twin-like pattern formation, providing insights into the mechanisms underlying chaos through fractional calculus operators including Caputo (C), Caputo–Fabrizio (CF), and Atangana–Baleanu Caputo (ABC) derivatives. A dynamical analysis was performed using Lyapunov exponents to examine the nature and stability of the system. Bifurcation analysis further elucidated the behavior of the system under varying parameters, revealing the emergence of coexisting attractors. We introduced a new time-based technique for studying coexisting attractors, which allowed us to investigate the dynamics of the system under different initial conditions. Electronic circuit simulations were employed to validate the theoretical predictions and provide a tangible platform for observing the chaotic dynamics in real time. The integration of a memristor-based function adds a novel dimension to this study, bridging the gap between chaos theory and electronics. Finally, we discuss the implications of the chaos theory on embryological growth through a fictional scenario involving chaos-based monozygotic embryological development. This imaginative exploration underscores the interdisciplinary nature of chaos theory and its potential applications across diverse fields, beyond traditional dynamical system analysis.</p>

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4D chaotic model with incommensurate circuits and fractional derivatives: fictional exhibition of monozygotic twins embryo growth

  • 期刊论文

  • 发表日期：

    2025年4月2日

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  • Muhammad Ali Qureshi,
  • Aiman Aziz,
  • Najeeb Alam Khan

摘要

This paper presents a novel 4D chaotic system characterized by the incorporation of a tangent hyperbolic memristor, which introduces additional nonlinearity into its dynamic framework. The system exhibits twin-like pattern formation, providing insights into the mechanisms underlying chaos through fractional calculus operators including Caputo (C), Caputo–Fabrizio (CF), and Atangana–Baleanu Caputo (ABC) derivatives. A dynamical analysis was performed using Lyapunov exponents to examine the nature and stability of the system. Bifurcation analysis further elucidated the behavior of the system under varying parameters, revealing the emergence of coexisting attractors. We introduced a new time-based technique for studying coexisting attractors, which allowed us to investigate the dynamics of the system under different initial conditions. Electronic circuit simulations were employed to validate the theoretical predictions and provide a tangible platform for observing the chaotic dynamics in real time. The integration of a memristor-based function adds a novel dimension to this study, bridging the gap between chaos theory and electronics. Finally, we discuss the implications of the chaos theory on embryological growth through a fictional scenario involving chaos-based monozygotic embryological development. This imaginative exploration underscores the interdisciplinary nature of chaos theory and its potential applications across diverse fields, beyond traditional dynamical system analysis.