The Melnikov method is a powerful analytical tool that predicts the onset of chaos in nonlinear dynamical systems by quantifying the separation between stable and unstable manifolds. Initially ...

Nonlinear control systems represent a critical area of study wherein the relationship between inputs and outputs is not directly proportional, resulting in complex and often unpredictable dynamics. In ...

Non-linear physics is the study of systems where the output is not directly proportional to the input. Unlike linear systems, which follow simple, predictable relationships, non-linear systems exhibit ...

Phonons are the quantum units of mechanical vibration. They describe how motion propagates through a solid at the smallest possible scales, in much the same way that electrons describe electric ...