Strange Attractor Type I
In this system, we have "connected" a feedback loop (Equation 3) to a van der Pol oscillator in its extended formulation:
dx/dt = 0.02 y + 0.4 x ( 0.2 - y2 ) (1)
dy/dt = - x + s z (2)
dz/dt = 10 x - 0.1 y (3)
Indeed, this system apparently simple since it embeds only one nonlinear term, i.e. xy2 , simulates a wide range of dynamics when varying the parameter s.
Simple but so rich !
Furthermore, this chaotic system was implemented in a specific electronic device:
Chaotic attractor exhibited by the circuit for s = 50:
projections on the (a) X–Z and (b) Y–Z phase planes
The Circuit design and its characteristics are introduced in the paper:
Emulating complex business cycles by using an electronic analogue, co-authored by S. Bouali, A. Buscarino, L. Fortuna, M. Frasca, and L.V. Gambuzza, Nonlinear Analysis: Real World Applications, 13 (2012), pp. 2459–2465.
The PDF version available here: nonlinear-analysis-bouali-et-al.pdf