2.1. Derivation Stage 2

Introduction
1. •
2. •
Derivation
1. •
2. •
3. •
4. •
Kuramoto
1. •
2. •
3. •
4. •
5. •
Simulator
1. •
Modifications
1. •
2. •
3. •
References
1. •
2. •

Suppose that you have N differential equations undergoing Hopf Bifurcation to stable oscillations and that these are globally, linearly coupled. Then we can write normal form coordinates for each oscillator.

where λ > 0. We now convert to polar co-ordinates by making the substitution z_k = r_k e^iθ_k, giving;

From here we divide both sides by e^iθ_k;