Perspectives on adaptive dynamical systems

Charles Darwin taught us that it is not the strongest of a species that survive, but the ones who are most adaptable to change. Like-wise, the process of learning can be considered to be "any changein a system that produces a more or less permanent change in its capacity for adapting to its environment."1 These two statements clearly underline the importance of adaptivity for life.Simply speaking, one could say: "To live means to adapt." At the same time, adaptive mechanisms are also the essential featuresof ("intelligent") artificial systems, from state-of-the-art control techniques for complex systems, to machine learning approachesand robotic systems. Perhaps the most basic notion of adaptivity is the ability to adjust to condition or change over time. Thisability is an essential component of various natural and artificial processes considered in different research fields. It is alsothe key property of the human mind to perceive and enjoy music and visual arts and to create and invent and, thus, is the driving force behind all cultural achievements. Adaptive mechanismstake place on a wide range of spatial and temporal scales, from the adaptation of a single neuron, over the ability of a social system to adjust to a changing environment, up to the adaptationof the Earth system's climate. Over the last few decades, substantial know-how to describe and control complex systems hasbeen developed in different scientific areas. With the increasing potential of modern technology, on the one hand, and the enormous challenges facing humanity as a large social system, on theother hand, there is a renewed interest to take an interdisciplinary approach to adaptivity. This article gives an overview of the role of adaptive systems in different scientific fields and highlightsprospects for future research directions on adaptivity.

Adaptivity is a dynamical feature that is omnipresent in nature, socio-economics, and technology. For example, adaptive couplings appear in various real-world systems, such as the power grid, social, and neural networks, and they form the backbone of closed-loop control strategies and machine learning algorithms. In this article, we provide an interdisciplinary perspective on adaptive systems. We reflect on the notion and terminology of adaptivity in different disciplines and discuss which role adaptivity plays for various fields. We highlight common open challenges and give perspectives on future research directions, looking to inspire interdisciplinary approaches.