CMMSE: Dynamics of a Current‐Carrying String in a Magnetic Field: Bifurcations, Time Series and Phase Portrait Analysis of the Mathieu‐Duffing Driven Oscillator

A string is a basic system for studying vibrations in a large variety of more complicated systems across diverse fields such as physics, electrical engineering and biology, providing mathematical techniques for their study and ideas for engineering applications. Electric current carrying string in a magnetic field has resulted in an even more complicated system that generated interesting nonlinear models such as the Mathieu‐Duffing (MD) driven oscillator studied in this work. We study the global dynamics of the MD driven oscillator, which naturally comes from the model of a stretched string under the influence of alternating electric current in a non‐uniform magnetic field. This system exhibits rich nonlinear dynamics that occur from the combined influence of thermal, electromagnetic, and elastic effects. We calculate time series, phase portraits and bifurcation diagrams (BDs) of inhomogeneous and adjoint homogeneous equations, numerically. We uncover the emergence of periodic, bistable, and multistable regimes, revealing the intricate transition between different states of the system. The global view through the time series, phase portraits and BDs of this multi‐parametric system is presented and discussed in this work. That gives an important framework for the deep insight in such systems and ideas for potential applications in physics and engineering.