Periodic solutions and circuit design of chaos in a unified stretch-twist-fold flow

Based on the original stretch-twist-fold flow, we propose a unified stretch-twist-fold (USTF) flow. We explore the conditions that zero-Hopf bifurcation occurs at the origin. Using the first-order averaging theorem, a periodic solution produced from the zero-Hopf equilibrium is derived. In addition, we obtain the conclusion that for parameter alpha large enough, the periodic orbit of USTF flow exists as well unstable. Finally, circuit design has been built for implementing the new system, showing a good agreement between computer simulations and experimental observations.

Automated summary

A new unified stretch-twist-fold flow is proposed, exploring conditions for zero-Hopf bifurcation and deriving a periodic solution from the zero-Hopf equilibrium using the first-order averaging theorem. For large enough parameter alpha, it is concluded that the periodic orbit of the USTF flow exists but is unstable. Experimental results show good agreement between circuit design, computer simulations, and experimental observations.