Coupled Oscillator Bifurcation
Two van der Pol oscillators coupled bidirectionally — explore Hopf bifurcations in phase space
Parameters
Coupling k
0.50
Damping μ
1.00
Freq ω₁
1.00
Freq ω₂
1.20
Speed
3
Limit Cycle
Van der Pol coupling:
ẍ₁ - μ(1-x₁²)ẋ₁ + ω₁²x₁ = k(x₂-x₁)
ẍ₂ - μ(1-x₂²)ẋ₂ + ω₂²x₂ = k(x₁-x₂)
μ<0: stable fixed point
μ=0: Hopf bifurcation
μ>0: limit cycle attractor
Reset Trajectories