OICC Press International Nano Letters 2228-5326 15 4 2026 02 01 Nonlinear Dynamical Band Structure Induced by Frequency-Dependent Nonlinearity in Duffing Oscillators 10.57647/inl.2025.1504.15 EN Morteza Abdollahi Sharif Optics and Laser Engineering Group, Faculty of Electrical Engineering, Urmia University of Technology, Urmia, Iran https://orcid.org/0000-0003-1469-6910 Mehdi Borjkhani Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland; International Centre for Translational Eye Research (ICTER), Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland Hadi Borjkhani Hochschule fur Technik und Wirtschaft Berlin, Berlin, Germany Journal Article 2026 02 01 We demonstrate that a nonlinear medium whose nonlinear susceptibility is explicitly frequency-dependent such as graphene-exhibits nonlinear dispersive dynamical states governed by the Duffing equation. These states selectively suppress or support certain frequency components of the driving field, forming a nonlinear band structure without any spatial periodicity. This reveals a new mechanism of nonlinear frequency filtering originating solely from the dynamical response of the nonlinear oscillator. The nonlinear dispersive mediummodifies the effective Floquet quasi-energy landscape of the driven Duffing oscillator. The Jacobi elliptic solutions exist only in regions where the nonlinear Floquet modes are stable, forming frequency-selective “nonlinear Floquet bands”. Outside these bands the Floquet multipliers diverge, resulting in forbidden frequencies.