Generalizing the twist-and-flip paradigm. II. (English) Zbl 0874.58073
Summary: [Part I appeared in ibid. 1, No. 2, 385-416 (1991; Zbl 0876.58033).]
We introduce a new concept, the control manifold, which simultaneously points us toward a general algorithm relating the existence of horseshoes in a Poincaré 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.
We introduce a new concept, the control manifold, which simultaneously points us toward a general algorithm relating the existence of horseshoes in a Poincaré 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.
MSC:
| 37N99 | Applications of dynamical systems |
| 93C15 | Control/observation systems governed by ordinary differential equations |
| 92B20 | Neural networks for/in biological studies, artificial life and related topics |
