Micro and nanomechanical systems are being adopted in billions of products, that address a wide range of sensor and actuator applications in modern technology. The advent of two-dimensional materials, and the ability to fabricate atomically thin membranes like graphene, promises further device downscaling, enabling ultimate sensing capabilities that until recently were only dreamed of. However, owing to their small size, these membranes exhibit nonlinearities at nm amplitudes and obtain a wealth of nonlinear phenomena whose potential in sensing applications are to be explored. Unlike common practice, this project will consider nonlinear dynamics not as phenomena to be avoided, but rather as new tools that can be exploited for betterment of nanomechanical performance. The project will include 2 PhD positions. The first PhD topic revolves around using nonlinear phenomena resulting from mode coupling, nonlinear dissipation or phase transitions to improve the performance of resonant sensors in closed loop. And for the second PhD topic the goal would be to understand and elucidate the phenomena that arise from the interplay between fluctuations and nonlinear dynamics. This will be achieved by thinning down 2D materials and manipulating their geometry such that intrinsic fluctuations already drive them into the nonlinear regime. Both projects will thus involve fabrication, testing, and nonlinear dynamic characterization of 2D material resonators and oscillators.