Frontiers in Complex Systems

Abstract

In this paper I intend to give an answer to three entangled questions: What is a Complex System?, What are present research challenges in Complex Systems?, and What is the purpose of the new journal Frontiers in Complex Systems?1. What is a Complex System? [1-3]Complexity comes from the Latin word “plexus” which indicates non-separability in components. Therefore, a good standard definition is that a Complex System is composed of many interacting units showing emerging properties that cannot be understood in terms of the properties of the individual isolated components. When we say that a system has emergent properties we mean that an effective theory of the system at some scale or level of organization is qualitatively different from the lower level scale. The slogan of Complex Systems is then that the whole is more than the sum of its parts (Aristole): Society is more than a collection of individuals, in the same way than brain and mind are more than a collection of neurons, or traffic a collection of cars. Complexity is not about things but about processes. It is about how order at large scales emerges from local interactions at small scales. Quoting the Nobel Laureate Phil W. Anderson [4], a reductionist hypothesis does not by any means imply a constructionist one: One can then say that, as a change of scientific paradigm, Complex Systems Science is the triumph of emergence over reductionism. In this sense it is not so much defined by a subject or specific system of research, but as a way to approach the understanding of systems behavior: Systems in which emergent behavior transcends the characteristics of the units composing the system are ubiquitous in many branches of natural sciences, human sciences and technology.A main important characteristic of Complex Systems behavior is that it is often associated with multiscale problems. Cities, the human body or economies have dynamics at very different scales. For example, coupled interactions in the brain cover nine orders of magnitude in spatial scales. How do we go from neurons, or below from the genome, to the brain functioning, or above, to human behavior?. Being more than the sum of its parts implies the existence of long-range correlations. The physics paradigm for these situations is the critical point of a phase transition, characterized by the divergence of the correlation length and by self-similar (scale free) behavior. The more challenging physical problems are precisely those embracing all scales. The lack of a characteristic scale is what makes a standard reductionist approach inappropriate and what gives rise to fat-tails and self-similar distributions that are common in Complex Systems description [5]. Additionally, a system in a critical point is at the threshold between order and disorder. The existence of a threshold indicates nonlinear behavior, and nonlinearity and half-way situations between order and disorder are also characteristics of Complex Systems.Emergent phenomena are conditioned by interaction networks describing which elements of the system interact with a given element. These Complex Networks [6,7] are the skeletons of Complex Systems and therefore an essential methodological ingredient for their description. Basic properties of these networks such as small-world (half-way between regular and random networks) or scale-free, share the complexity fingerprints of a critical point. Taking into account the dynamical adaptability as another characteristic of Complex System behavior, a mathematical definition of Complex Systems has been given as co-evolving multilayer networks [1].Another important characteristic of Complex Systems is that there are intrinsic limits for long time quantitative predictions of their behavior. The issue of predictability is a main link between the two parts of the 2021 Nobel Prize in Physics awarded "for groundbreaking contributions to our understanding of complex systems", with one half jointly to Syukuro Manabe and Kl