# Math Help - Rikitake model

1. ## Rikitake model

for the system

dx/dt= -vx+zy
dy/dt= -vy+(z-a)x
dz/dt= 1-xy

a,v are positive parameter.

after finding the fixed points, how am i supposed to classify them??
Should I build a 3*3 matrix??
If so, how am I supposed to take derivative, cuz there are non-linear turms like zy and xy????????????????

Thanks

2. Originally Posted by felixmcgrady
for the system

dx/dt= -vx+zy
dy/dt= -vy+(z-a)x
dz/dt= 1-xy

a,v are positive parameter.

after finding the fixed points, how am i supposed to classify them??
Should I build a 3*3 matrix??
If so, how am I supposed to take derivative, cuz there are non-linear turms like zy and xy????????????????

Thanks
Yes, your 3X3 matrix is the Jacobian matrix. Sub in your critical points and then look at the eigenvalues of the matrix, this will give you the stablility of the critical point.