Dynamical systems in wireless communications: The road less traveled by

Dynamical systems are by no means strangers in wireless communications, but we sometimes tend to forget how rich their behavior can be and how useful general methods for dynamical systems can be. Our story will necessarily involve chaos, but not in the terms secure chaotic communications have introduced it: we will look for the chaos, complexity and dynamics that already exist in everyday wireless communications. We present a short overview of dynamical systems and chaos before focusing on the applications of dynamical systems theory to wireless communications in the past 30 years, ranging from the modeling on the physical layer to different kinds of self-similar traffic encountered all the way up to the network layer. The examples of past research and its implications are grouped and mapped onto the media layers of ISO OSI model to show just how ubiquitous dynamical systems theory can be and to trace the paths that may be taken now. When considering the future paths, we argue that the time has come for us to revive the interest of the research community to dynamical systems in wireless communications. We might have avoided those paths earlier because of the big question: can we afford observing systems of our interest as dynamical systems and what are the trade-offs? The answers to these questions are dynamical systems of its own: they change not only with the modeling context, but also with time. In the current moment, we argue, the available resources allow such approach and the current demands ask for it. The results we obtained standing on the shoulders of dynamical systems theory suggest the necessity for its inclusion in the wireless toolbox for the highly dynamical world of 5G and beyond.