A new chaos detector

This paper proposes a new detector for chaos. It is simpler and numerically less intensive than previous methods. It is more robust than previous methods. It works well even with short data sets (200 time scalar points), in the presence of noise (as low as 4 dB signal to noise ratio in stationary additive white Gaussian noise), and with severe data level quantization (data quantized to five bits). The theory behind the new detector is given, and examples of its application to the Logistic, Henon, and Lozi Maps are shown. The new chaos detector is briefly compared to existing methods such as the estimation of the largest Lyapunov exponent, the correlation or attractor dimension, and the entropy of the data set. Conventional electrical engineering signal analysis tools (such as the Discrete Fourier Transform) fail to help in the detection of chaos. This failure is explored. Sinusoids and several types of noise are input to the detector and the outputs are recorded. The basis for a binary signaling scheme which uses chaotic sequences and the new chaos detector is briefly described.