A Hopf bifurcation occurs when a complex-conjugate pair of eigenvalues crosses the imaginary axis and a periodic orbit is created or destroyed near the equilibrium.
Hopf bifurcation is a critical phenomenon in dynamical systems that occurs when a system's stability changes, leading to the emergence of oscillatory behavior. It specifically involves the transition from a stable equilibrium point to a stable limit cycle or periodic orbit as certain system parameters are varied. To understand Hopf bifurcation in more detail, consider a dynamical system described by ordinary differential equations.
New to topics? Read the docs here!