Hamilton Energy Characteristics of Chaotic Systems and Energy Flow in Magnetically Coupled Circuits

This paper systematically investigates the Hamiltonian characteristics of chaotic attractors in nonlinear circuits and elucidates the intrinsic energy transfer mechanisms in magnetically coupled nonlinear systems using generalized Hamiltonian theory. First, Hamiltonian properties of the Modified Van der Pol-Duffing (MVDPD) system, improved memristive Chua’s system, and Colpitts-derived Chua’s system are analyzed, establishing a unified relationship between system dynamics and Hamilton energy characteristics. Next, through numerical analysis, circuit simulation, and experimental validation, we investigate the internal mechanisms underlying energy exchange and dynamic evolution in magnetically coupled nonlinear circuits. Results demonstrate significant changes in energy exchange behaviors during phase synchronization. Specifically, the energy cost required for synchronization initially rises, peaks during the onset of synchronization, and then declines with improved internal coherence. These findings provide valuable insights into energy flow dynamics in magnetically coupled nonlinear circuits.