Otro
Dynamic behavior of a simple canonical system
Autor
Binous, Housam
Resumen
Consider the following system of ODEs: dx/dt=αx+βy; dy/dt=-βx+αy. The eigenvalues of this simple canonical system are λ=α+-βi. The extremum, M=(0,0), is shown as a green dot.
If α>0, the extremum is an unstable focus.
If α<0, the extremum is a stable focus.
If α=0, the dynamic behavior is that of a limit cycle and the critical point is a center.
If β>0, the trajectories spiral clockwise around the origin.
If β<0, the trajectories spiral counterclockwise around the origin.
The red curve is the parametric plot of the solution of the system of ODEs with an initial condition P=(1,1)(shown as a cyan dot). Educação Superior::Ciências Exatas e da Terra::Matemática