Multiscale analysis to facilitate joint chaos and fractal analysis of biosignals

Biological systems provide definite examples of multiscale systems, which generate nonlinear, non-stationary, and highly complex signals. Developing effective methods for biosignal analysis has become increasingly important, owing to rapid progress in biosensing and astronomical accumulation of biological data. Albeit chaos and random fractal theories are among the most popular and most promising methods for biosignal analysis, they often may not be directly applicable, since chaos analysis requires that signals be relatively noise-free and stationary, and fractal analysis demands signals to be non-rhythmic and scale-free, which are rarely true in biology. We propose two multiscale approaches for biosignal analysis, adaptive fractal analysis and scale-dependent Lyapunov exponent (SDLE) analysis, and show that together they can tremendously facilitate joint chaos and multiscale analysis of biosignals.