Chaotic systems that are robust to added noise

While added noise can destroy synchronization in synchronized chaotic systems, it was shown that some chaotic systems were not sensitive to added noise. In this paper, the mechanism for this noise resistance is explored. It is seen that part of the chaotic system acts like it is resonant, reducing the noise sensitivity of the system. By comparing to a model of a neuron, it is speculated that similar mechanisms may also be present in biological systems.

Chaotic control and synchronization for system identification

Research into applications of synchronized chaotic systems assumes that it will be necessary to build many different drive-response pairs, but little is known in general about designing higher dimensional chaotic flows. In this paper, I do not add any design techniques, but I show that it is possible to create multiple drive-response pairs from one chaotic system by applying chaos control techniques to the drive and response systems. If one can design one chaotic system with the desired properties, then many drive-response pairs can be built from this system, so that it is not necessary to solve the design problem more than once. I show both numerical simulations and experimental work with chaotic circuits. I also test the response systems for ability to overcome noise or other interference.

Chaotic communications that are difficult to detect

Work on self-synchronizing systems for communications has had limited practicality because the chaotic signals were not as easy to detect in the presence of noise as conventional spread-spectrum signals. This difficulty may actually be an advantage in some cases, where one wants to conceal the existence of the communications signal. Conventional communications signals are cyclostationary; while they may look random, they have statistical properties that vary periodically. One may design chaotic communication signals that lack this cyclostationary property, and therefore are harder to detect.

Using unstable periodic orbits to overcome distortion in chaotic signals

Proposals to use chaos for communications have been hindered by the fact that broadband chaotic signals are distorted by narrow band or frequency dependent communications channels. I show in this paper how the unstable periodic orbits from a chaotic attractor may be used to estimate the parameters of a filter that has acted on a signal from that attractor and estimate the chaotic signal, even when additive noise larger than the chaotic signal is present.