<p>Accurate parameter identification in chaotic dynamical systems constitutes a challenging inverse problem due to extreme sensitivity to initial conditions, pronounced nonlinearity, and highly multimodal error landscapes. To address these challenges, this study proposes a global-best-guided electric eel foraging optimization algorithm (g-EEFO), which enhances the original EEFO framework by embedding a behavior-aware and phase-dependent global learning mechanism. Unlike existing EEFO variants that rely solely on stochastic foraging dynamics, g-EEFO integrates global-best information as a soft cooperative signal that modulates the interacting, resting, hunting, and migrating behaviors without overriding them. In this way, global guidance acts as a directional bias rather than a dominant attractor, preserving ecological diversity while strengthening convergence coherence. For the first time, EEFO and its improved variant are applied to chaotic system parameter estimation. The proposed method is evaluated on two representative models: the classical Lorenz system and a structurally richer memristive chaotic system. Extensive numerical experiments, including statistical analysis, convergence profiling, boxplot distributions, and parameter-evolution trajectories, demonstrate the clear superiority of g-EEFO over several state-of-the-art metaheuristics. For the Lorenz system, g-EEFO achieves a best mean squared error of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:7.02\times\:{10}^{-26}\)</EquationSource> </InlineEquation>, which is six to twenty orders of magnitude lower than competing methods, while maintaining an exceptionally small standard deviation (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:4.58\times\:{10}^{-20}\)</EquationSource> </InlineEquation>). For the memristive system, g-EEFO attains a best error of <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\:8.19\times\:{10}^{-19}\)</EquationSource> </InlineEquation>, again outperforming all benchmarks by several orders of magnitude and exhibiting the highest run-to-run stability. In both cases, the estimated parameters match the true system values with near-perfect precision. These results confirm that the proposed behavior-aware global guidance fundamentally reshapes the search dynamics of EEFO, yielding substantial gains in convergence stability, numerical accuracy, and robustness. The g-EEFO therefore provides a powerful and reliable alternative for chaotic parameter identification and nonlinear system reconstruction across diverse dynamical regimes.</p>

Global-best-guided electric eel foraging optimizer for robust parameter identification of Lorenz and memristive chaotic systems

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2026年2月12日

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Davut Izci,
Serdar Ekinci,
İrfan Ökten,
Vedat Tümen,
Burcu Bektaş Güneş,
Mostafa Rashdan,
Mohammad Salman

摘要

Accurate parameter identification in chaotic dynamical systems constitutes a challenging inverse problem due to extreme sensitivity to initial conditions, pronounced nonlinearity, and highly multimodal error landscapes. To address these challenges, this study proposes a global-best-guided electric eel foraging optimization algorithm (g-EEFO), which enhances the original EEFO framework by embedding a behavior-aware and phase-dependent global learning mechanism. Unlike existing EEFO variants that rely solely on stochastic foraging dynamics, g-EEFO integrates global-best information as a soft cooperative signal that modulates the interacting, resting, hunting, and migrating behaviors without overriding them. In this way, global guidance acts as a directional bias rather than a dominant attractor, preserving ecological diversity while strengthening convergence coherence. For the first time, EEFO and its improved variant are applied to chaotic system parameter estimation. The proposed method is evaluated on two representative models: the classical Lorenz system and a structurally richer memristive chaotic system. Extensive numerical experiments, including statistical analysis, convergence profiling, boxplot distributions, and parameter-evolution trajectories, demonstrate the clear superiority of g-EEFO over several state-of-the-art metaheuristics. For the Lorenz system, g-EEFO achieves a best mean squared error of \(\:7.02\times\:{10}^{-26}\) , which is six to twenty orders of magnitude lower than competing methods, while maintaining an exceptionally small standard deviation ( \(\:4.58\times\:{10}^{-20}\) ). For the memristive system, g-EEFO attains a best error of \(\:8.19\times\:{10}^{-19}\) , again outperforming all benchmarks by several orders of magnitude and exhibiting the highest run-to-run stability. In both cases, the estimated parameters match the true system values with near-perfect precision. These results confirm that the proposed behavior-aware global guidance fundamentally reshapes the search dynamics of EEFO, yielding substantial gains in convergence stability, numerical accuracy, and robustness. The g-EEFO therefore provides a powerful and reliable alternative for chaotic parameter identification and nonlinear system reconstruction across diverse dynamical regimes.