This third of three volumes presents papers from the fourth series of the NODYCON conferences held at Stevens Institute of Technology, Hoboken, NJ, USA, in June of 2025. The conference papers reflect a broad coverage of traditional topics in nonlinear dynamics as well as newly established and emerging streams of research. These include

• Composite/nanocomposite structures for dynamics: damping, modeling, dynamics

• Metamaterials and programmable/multifunctional structures

• NEMS/MEMS and nanomaterials: multi-sensors, actuators exploiting nonlinear working principles

• Systems with time and/or space delays

• Fractional-order system dynamics

• Advanced cryptography based on chaotic maps

• Ecosystem dynamics, social media dynamics (user behavior dynamics in multi-messages social hotspots, prediction models), complexity in engineering. Cutting-Edge Integration of AI and Data-Driven Dynamics; Multidisciplinary Approach to Nonlinear Systems; Real-World Application Focus with Engineering Innovations.