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Pivots of the pendulums are coupled by an elastic element. The magnetic interaction originates from permanent magnets, mounted at free ends of the pendulums and current-powered air coils underneath. A novel model for the magnetic force is proposed and verified experimentally. Nonlinear dynamics of the system is examined by means of time series, bifurcation diagrams, phase portraits, and Poincar\u00e9 sections. Regions of chaotic and regular motion are predicted numerically and justified experimentally. 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