Complex system
A complex system is a system composed of many components that interact with one another. Examples of complex systems are Earth's global climate, organisms, the human brain, infrastructure such as power grid, transportation or communication systems, complex software and electronic systems, social and economic organizations, an ecosystem, a living cell, and, ultimately, for some authors, the entire universe.
The behavior of a complex system is intrinsically difficult to model due to the dependencies, competitions, relationships, and other types of interactions between their parts or between a given system and its environment. Systems that are "complex" have distinct properties that arise from these relationships, such as nonlinearity, emergence, spontaneous order, adaptation, and feedback loops, among others. Because such systems appear in a wide variety of fields, the commonalities among them have become the topic of their independent area of research. In many cases, it is useful to represent such a system as a network where the nodes represent the components and links represent their interactions.
The term complex systems often refers to the study of complex systems, which is an approach to science that investigates how relationships between a system's parts give rise to its collective behaviors and how the system interacts and forms relationships with its environment. The study of complex systems regards collective, or system-wide, behaviors as the fundamental object of study; for this reason, complex systems can be understood as an alternative paradigm to reductionism, which attempts to explain systems in terms of their constituent parts and the individual interactions between them.
As an interdisciplinary domain, complex systems draw contributions from many different fields, such as the study of self-organization and critical phenomena from physics, of spontaneous order from the social sciences, chaos from mathematics, adaptation from biology, and many others. Complex systems is therefore often used as a broad term encompassing a research approach to problems in many diverse disciplines, including statistical physics, information theory, nonlinear dynamics, anthropology, computer science, meteorology, sociology, economics, psychology, and biology.
Types of systems
Complex systems can be:- Complex adaptive systems which have the capacity to change,
- Polycentric systems "where many elements are capable of making mutual adjustments for ordering their relationships with one another within a general system of rules where each element acts with independence of other elements",
- Disorganised systems which involve localized interactions of multiple entities that do not form a coherent whole. Disorganised systems are linked to self-organisation processes.
- Hierarchic systems which are analyzable into successive sets of subsystems. They can also be called nested or embedded systems.
- Cybernetic systems which involve information feedback loops.
Key concepts
Adaptation
s are special cases of complex systems that are adaptive in that they have the capacity to change and learn from experience. Examples of complex adaptive systems include the international trade markets, social insect and ant colonies, the biosphere and the ecosystem, the brain and the immune system, the cell and the developing embryo, cities, manufacturing businesses and any human social group-based endeavor in a cultural and social system such as political parties or communities.Decomposability
A system is decomposable if the parts of the system are independent from each other, for example the model of a perfect gas consider the relations among molecules negligible.In a nearly decomposable system, the interactions between subsystems are weak but not negligible, this is often the case in social systems. Conceptually, a system is nearly decomposable if the variables composing it can be separated into classes and subclasses, if these variables are independent for many functions but affect each other, and if the whole system is greater than the parts.
Features
Complex systems may have the following features:;Complex systems may be open
;Complex systems may exhibit critical transitions
;Complex systems may be nested
;Dynamic network of multiplicity
File:Gospers glider gun.gif|frame|right|Gosper's Glider Gun creating "gliders" in the cellular automaton Conway's Game of Life
; May produce emergent phenomena
; Relationships are non-linear
; Relationships contain feedback loops
History
In 1948, Dr. Warren Weaver published an essay on "Science and Complexity", exploring the diversity of problem types by contrasting problems of simplicity, disorganized complexity, and organized complexity. Weaver described these as "problems which involve dealing simultaneously with a sizable number of factors which are interrelated into an organic whole."While the explicit study of complex systems dates at least to the 1970s, the first research institute focused on complex systems, the Santa Fe Institute, was founded in 1984. Early Santa Fe Institute participants included physics Nobel laureates Murray Gell-Mann and Philip Anderson, economics Nobel laureate Kenneth Arrow, and Manhattan Project scientists George Cowan and Herb Anderson. Today, there are over 50 institutes and research centers focusing on complex systems.
Since the late 1990s, the interest of mathematical physicists in researching economic phenomena has been on the rise. The proliferation of cross-disciplinary research with the application of solutions originated from the physics epistemology has entailed a gradual paradigm shift in the theoretical articulations and methodological approaches in economics, primarily in financial economics. The development has resulted in the emergence of a new branch of discipline, namely "econophysics", which is broadly defined as a cross-discipline that applies statistical physics methodologies which are mostly based on the complex systems theory and the chaos theory for economics analysis.
The 2021 Nobel Prize in Physics was awarded to Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi for their work to understand complex systems. Their work was used to create more accurate computer models of the effect of global warming on the Earth's climate.
Applications
Complexity in practice
The traditional approach to dealing with complexity is to reduce or constrain it. Typically, this involves compartmentalization: dividing a large system into separate parts. Organizations, for instance, divide their work into departments that each deal with separate issues. Engineering systems are often designed using modular components. However, modular designs become susceptible to failure when issues arise that bridge the divisions.Complexity of cities
Jane Jacobs described cities as being a problem in organized complexity in 1961, citing Dr. Weaver's 1948 essay. As an example, she explains how an abundance of factors interplay into how various urban spaces lead to a diversity of interactions, and how changing those factors can change how the space is used, and how well the space supports the functions of the city. She further illustrates how cities have been severely damaged when approached as a problem in simplicity by replacing organized complexity with simple and predictable spaces, such as Le Corbusier's "Radiant City" and Ebenezer Howard's "Garden City". Since then, others have written at length on the complexity of cities.Complexity economics
Over the last decades, within the emerging field of complexity economics, new predictive tools have been developed to explain economic growth. Such is the case with the models built by the Santa Fe Institute in 1989 and the more recent economic complexity index, introduced by the MIT physicist Cesar A. Hidalgo and the Harvard economist Ricardo Hausmann.Recurrence quantification analysis has been employed to detect the characteristic of business cycles and economic development. To this end, Orlando et al. developed the so-called recurrence quantification correlation index to test correlations of RQA on a sample signal and then investigated the application to business time series. The said index has been proven to detect hidden changes in time series. Further, Orlando et al., over an extensive dataset, shown that recurrence quantification analysis may help in anticipating transitions from laminar to turbulent phases such as USA GDP in 1949, 1953, etc. Last but not least, it has been demonstrated that recurrence quantification analysis can detect differences between macroeconomic variables and highlight hidden features of economic dynamics.