Experimental complexity in physical, social and biological systems

There are a myriad of examples of dynamical systems displaying chaos and complex behavior, from the simple double pendulum, to the much more complex human brain or any social organization. They are typically characterized by the presence of nonlinear interactions governing their often unpredictable dynamical evolution, which makes it impossible to provide a simple description of their behavior even under controlled laboratory conditions. The very first (published) evidence of chaos in an experimental system was reported in 1977 by Jack Hudson and collaborators, who observed sustained time-dependent nonperiodic oscillations in the Belousov–Zhabotinsky reaction in a continuous-flow stirred reactor [1]. Before that, chaotic dynamics had been first noticed and recorded by Yoshisuke Ueda during his Ph.D. at the end of 1961 in an electronic realization of a driven Duffing oscillator —however, this work was only published in 1992 [2]. Other milestones of this early research into complex dynamical behavior include David Ruelle and Floris Takens’ investigations into the mechanisms underlying turbulence. They introduced the term “strange attractor” and proposed theoretically that the transition to turbulence should be observed after just three or four bifurcations [3], and Gollub and Swinney showed experimentally that this mathematical result could be possibly observed in a rotating fluid [4]. A few years later, intermittences [5] and the routes to chaos [6] were found in a Rayleigh–Bénard experiment. After that, chaotic behavior was observed in many different fields of research, such as laser and nonlinear optics physics [7], [8], [9], plasma physics [10] and even in astrophysics [11]. Whether chaos is observed in biomedical data is still an open question, mostly because it is rather difficult to provide a conclusive proof for an underlying determinism [12]. Finally, while much of this experimental work concerns itself with temporal chaos, turbulence is complexity not only in time but also in space, and from its study the new field of spatio-temporal chaos and pattern formation in hydrodynamic systems emerged [13], [14].