Anomalous Gilbert damping and Duffing features of the superconductor-ferromagnet-superconductor <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>?</mml:mi><mml:mn>0</mml:mn></mml:msub></mml:math> Josephson junction

We demonstrate unusual features of phase dynamics, IV-characteristics and magnetization dynamics the $\varphi_0$ Josephson junction at small values spin-orbit interaction, ratio to magnetic energy Gilbert damping. In particular, an anomalous shift ferromagnetic resonance frequency with increase damping is found. The curves show Duffing oscillator behaviour, reflecting nonlinear nature Landau-Lifshitz-Gilbert (LLG) equation. Based on numerical analysis each term in LLG equation we obtained approximated demonstrated both effect features. resulting incorporates a special way across dissipative restoring force. A method for determination interaction noncentrosymmetric materials which play role barrier junctions proposed.