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Exploring Chameleon Chaos: A Linearly Modulated Generalized Duffing System with Hidden and Self-Excited Attractors.

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Title: Exploring Chameleon Chaos: A Linearly Modulated Generalized Duffing System with Hidden and Self-Excited Attractors.
Authors: Liu, Xueqing1 (AUTHOR), Sang, Bo1 (AUTHOR) sangbo_76@163.com, Wang, Chun1 (AUTHOR), Wang, Cuicui1 (AUTHOR), Liu, Yan1 (AUTHOR), Yang, Cuihong2,3 (AUTHOR), Ahmad, Irfan4 (AUTHOR), Karimov, Timur5 (AUTHOR), Rybin, Vyacheslav5 (AUTHOR), Butusov, Denis5 (AUTHOR), Wang, Ning6 (AUTHOR)
Source: International Journal of Bifurcation & Chaos in Applied Sciences & Engineering. May2026, Vol. 36 Issue 6, p1-19. 19p.
Subjects: Duffing equations, Attractors (Mathematics), Chaos theory, Bifurcation theory, Hopf bifurcations
Abstract: This paper presents a novel chameleon chaotic system derived from a generalized Duffing oscillator, where the linear damping parameter c controls the transition between hidden and self-excited attractors. The investigation covers the system's basic properties, including symmetries, dissipativity, and equilibrium stability, where the stability analysis identifies a supercritical Hopf bifurcation at c = 0 as the transition mechanism. This bifurcation helps to find two potential dynamical regimes: for c ≤ 0 , the system may exhibit hidden attractors coexisting with a stable equilibrium; for c > 0 , self-excited attractors can arise from the unstable equilibrium. By setting several parameters to fixed values, including the critical condition c = 0 , we define the model's reduced system with an elegant form. A detailed analysis of this system using bifurcation and continuation diagrams, Lyapunov exponents, return map, and power spectrum shows the existence of a hidden chaotic attractor and reveals rich multistability behavior. Bifurcation studies across multiple parameter planes demonstrate period-doubling cascades to chaos, periodic windows, and complex dynamical landscapes. Finally, the phase portraits produced by an FPGA-based realization closely match numerical simulations, thus enabling our manageability of the chameleon dynamics. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:This paper presents a novel chameleon chaotic system derived from a generalized Duffing oscillator, where the linear damping parameter c controls the transition between hidden and self-excited attractors. The investigation covers the system's basic properties, including symmetries, dissipativity, and equilibrium stability, where the stability analysis identifies a supercritical Hopf bifurcation at c = 0 as the transition mechanism. This bifurcation helps to find two potential dynamical regimes: for c ≤ 0 , the system may exhibit hidden attractors coexisting with a stable equilibrium; for c > 0 , self-excited attractors can arise from the unstable equilibrium. By setting several parameters to fixed values, including the critical condition c = 0 , we define the model's reduced system with an elegant form. A detailed analysis of this system using bifurcation and continuation diagrams, Lyapunov exponents, return map, and power spectrum shows the existence of a hidden chaotic attractor and reveals rich multistability behavior. Bifurcation studies across multiple parameter planes demonstrate period-doubling cascades to chaos, periodic windows, and complex dynamical landscapes. Finally, the phase portraits produced by an FPGA-based realization closely match numerical simulations, thus enabling our manageability of the chameleon dynamics. [ABSTRACT FROM AUTHOR]
ISSN:02181274
DOI:10.1142/S0218127426500744