Nonlinear Dynamics and Chaos in Mechanical Oscillatory Systems

Nonlinear dynamics and chaos could not be for complex behaviour. Such behaviour leads to oscillations in mechanical systems. Due to the overwhelming influence of chaotic behaviour in such systems, the present paper was carried out mostly theoretically and computationally-chaos mostly from huffing oscillator and its mechanical implementations. In addition, with the setup of experimental wide-parameters robust chaotic oscillations (Karimov et al., 2023) a new mechanical scheme realization in magnetic springs has been opened. Furthermore, from theoretical point of view there are recent papers that have revealed the transition from periodic to chaotic dynamics via period-doubling and bifurcation in hyperbolic double-well Duffing-type oscillators (Author et al., 2025). Inferring hidden dynamics framework is a new approach to predict observable and hidden variables from complex oscillatory systems (Stepanian’s et al., 2024). Therefore, in the paper we have decided to integrate these ideas and recent results from 2023 to 2025, and to carry out the following recent analysis of nonlinear behaviour, have looked at what approaches were used to detect chaos (through bifurcation diagrams, Lyapunov exponents, Poincare maps), and what the implications are for vibration control, fault diagnosis, and energy harvesting.