Editorial: Nonlinear dynamics and networks in sports

Evolution, self-organization, synchronization, entropy, or chaos are traditionally related to statistical physics and applied mathematics. Although their early developments came up from systems exclusively of these branches of knowledge, the applications of the methodologies quantifying the appearance of such phenomena in other real systems are increasing from year to year. Among these, Sports Science is one of the beneficiaries of the high applicability of Complexity Sciences. This fact is becoming more evident due to the recent ability to capture a diversity of new variables thanks to new technological advances. In this way, it is possible to record the speed of a ball during a tennis match, the strokes’ position, the distances ran by each player and the corresponding velocities. In team games, such as football, we can track the position of the twenty-two players and the ball at a resolution of 25 frames per second, which results in large datasets containing priceless information about each team (and player) style of playing. However, how to extract useful information from such large datasets? The answer is not simple and, on the contrary, it implies an analysis based on the complexity of the systems under study. Furthermore, it requires the effort of mathematicians, physicists, data-analysts and sports scientists united in a common framework in order to adapt classical (and not so classical) methodologies coming from nonlinear dynamics [1] or network science [2] to the analysis of sports. Despite there is a vast literature about nonlinear analysis of sports datasets, recent advances in such fields, such as multilayer networks [3], chimera [4] or Bellerophon states [5], explosive synchronization [6] or controllability of networks [7] (to mention a few) make necessary a new revision of how sports science can benefit from them. Specifically, the current Special Issue is focused on the use of nonlinear dynamics and networks models in order to improve the knowledge and practical applications about teams and athletes/players’ performance during trainings and competitions.