System ẋ = f(x,μ): complex-conjugate eigenvalues cross imaginary axis → birth of periodic orbit. Normal form classification; super/subcritical.
Hopf bifurcation
Related concepts
- Ordinary differential equation (ODE)
- Logistic map (Feigenbaum 1975)
- Laser rate equations & threshold
- Memristors & neuromorphic computing
- Wilson-Cowan 2-pop: τ·dE/dt=−E+S(w·inputs); Hopf bifurcation at σ_H=2/(w_EE−w_II)
- Punctuated equilibrium
- CDK bistable switch (Tyson-Novak)
- Apoptosis bistable switch (Eissing model)
- HPG pulsatile oscillator
- Quorum sensing bistable autoinducer threshold
- Genetic toggle switch (Gardner-Collins) bistability
- Repressilator (Elowitz-Leibler oscillator)
- Synthetic circuit dynamics (Elowitz-Leibler design rules)
- Notch-Delta lateral inhibition
- Wilson-Cowan neural-mass (1972)
- p53 tumor suppressor (Vogelstein 1989)
- Alternative stable states (Scheffer 2001)