Thermo-mechanically coupled Duffing oscillator: Heating, feedback, and attractor dynamics

A Duffing oscillator whose effective stiffness is dynamically modified through thermodynamic coupling, resulting in a temperature-dependent nonlinear response, is analyzed. In contrast to the classical Duffing model with a prescribed cubic nonlinearity, the restoring force in this system evolves through temperature-driven feedback. To characterize the resulting dynamics, stroboscopic sampling combined with a normalized cardinality measure is employed to classify attractors and construct detailed dynamical-regime maps in the thermal-capacity-thermal-cooling parameter space. The analysis identifies periodic, quasi-periodic, and chaotic responses and reveals systematic shifts in the dominant attractor types as thermal parameters vary. These results show that thermomechanical coupling can substantially modify the oscillator's nonlinear behavior and lead to attraction structures that differ from those observed in the standard Duffing formulation.