GENERALIZING THE TWIST-AND-FLIP PARADIGM: II

In this letter we introduce a new concept, the control manifold, which simultaneously points us toward a general algorithm relating the existence of horseshoes in a Poincare map to the parameters of an ODE, while also providing a mechanism for understanding how to control nonlinear phenomena and therefore utilize these phenomena in a disciplined and predictable manner in the design of nonlinear circuits, systems, and neural networks.