Hopf Bifurcation

A Hopf bifurcation is a mathematical concept describing a situation where a system's behavior changes from stable and steady to oscillatory and periodic as a parameter is varied. Imagine a pendulum at rest; adjusting a factor like energy input can cause it to start swinging regularly. Similarly, in systems like neural networks or circuits, small changes can lead to the emergence of continuous, rhythmic activity. It marks the point where a steady state loses stability and gives rise to regular, repeating oscillations, helping scientists understand how complex periodic behaviors originate from stable conditions.