A systematic framework for classification of parameter space dynamics in the Duffing oscillator

This paper introduces a systematic framework for classifying the parameter space of the Duffing oscillator into three distinct levels. The first level categorizes the parameter space based on statistical properties, identifying diverging, non-diverging, and fixed point attractors. The second level focuses on the nature of the eigenvalues. In this paper, nine distinct types and their corresponding parameter ranges are identified. Finally, the third level classifies chaotic and periodic behaviors using Lyapunov exponents. For a single initial state, 19965 cases are analyzed, revealing that most of the parameter space is diverging, with few regions of nondiverging cases, highlighting the importance of precise design decisions to remain in stable regions. With the variation in initial states, the category distribution also varies across the parameter space. To this end, the analysis of selected cases from classification results is conducted using tools: attractors, multistability, time series, Lyapunov exponents, binary mapping, return map, Poincaré map, and power spectrum. In addition, the representation of behavior across classified parameter space is obtained. Moreover, the design choices made to replicate the behavior of the Duffing oscillator in its electrical circuit counterpart are presented, ensuring alignment in their dynamic responses. Hardware experiments validated the chaotic and periodic behaviors under varying conditions. The comprehensive dataset including attractors, Lyapunov exponents, and categorized parameter space is created that can be used in the future and offers a valuable resource for engineers and researchers. • A systematic framework for the classification of behavior of nonlinear systems is proposed. • The proposed method is validated using the Duffing oscillator and its electrical circuit. • Behavior representation is obtained using various chaos detection techniques. • A comprehensive categorized dataset is created.