While the synchronization of regular oscillators with limit cycle attractors is ubiquitous in Nature, the synchronization of loosely coupled chaotic oscillators has been studied only recently. In this two-part talk, I will discuss applications and potential applications of synchronized chaos to the foundations of quantum theory, atmospheric dynamics, and biologically-motivated neural network architectures.
In Part I, starting with a review of Bell's Theorem, I will explore an analogy between quantum cryptography and a form of cryptography based on synchronized chaos. In one such scheme, two variable-order Generalized Rossler Systems will synchronize when coupled through only one of many variables. But in the infinite-order limit, the dynamical parameters of the driving system cannot be extracted in finite time. The phenomenon supports the possibility of an interpretation of quantum mechanics in which quantum nonlocality is mediated by supraluminal connections that are real, but perfectly disguised.