This third of three volumes from the inaugural NODYCON, held at the University of Rome, in February of 2019, presents papers devoted to New Trends in Nonlinear Dynamics. The collection features both well-established streams of research as well as novel areas and emerging fields of investigation. Topics in Volume III include NEMS/MEMS and nanomaterials: multi-sensors, actuators exploiting nonlinear working principles, adaptive, multifunctional, and meta material structures, nanocomposite structures (e.g., carbon nanotube/polymer composites, composites with functionalized nanoparticles), 0D, 1D, 2D, 3D nanostructures, biomechanics applications, DNA modeling, walking dynamics, heart dynamics, neurodynamics, capsule robots, jellyfish-like robots, nanorobots, cryptography based on chaotic maps, ecosystem dynamics, social media dynamics (user behavior dynamics in multi-messages social hotspots, prediction models), financial engineering, complexity in engineering, and network dynamics (multi-agent systems, leader-follower dynamics, swarm dynamics, biological networks dynamics).