Multifractal Signal Generation by Cascaded Chaotic Systems and Their Analog Electronic Realization

Multifractality, that is, self-similarity where in scaling follows a continuous spectrum of exponents, is a ubiquitous property of the morphology and dynamics of large-scale complex systems. However, to date, the prerequisites for the generation of multifractal time series by dynamical systems remain an open issue. This work demonstrates that multifractality can emerge in the time series spontaneously generated by a small ensemble of cascaded nonlinear oscillators, which are deterministic, autonomous and delayless. Namely, a chain of four Rössler systems with directed couplings is investigated numerically and realized experimentally in the form of analog electronic circuits. The observation of multifractality is established using the detrended fluctuation analysis and confirmed through surrogate tests, wavelet-based analyses and cascade structure visualization. Multifractality consistently arises when the oscillation frequencies of the coupled oscillators span a sufficient range along the chain, and the couplings have an intermediate strength which engenders partial entrainment between the adjacent nodes. These results affirm that neither external entropy injection nor driving are indispensable, and provide a blueprint for the design of self-contained generative circuits toward diverse applications across physiology modeling and unconventional computing.