Complex system

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. • Hierarchical 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 Complex adaptive systems are special cases of complex systems that are adaptive in that they have the capacity to change and learn from experience. ==Features==

Complex systems may have the following features: ;Complex systems may be open : Complex systems are usually open systems – that is, they exist in a thermodynamic gradient and dissipate energy. In other words, complex systems are frequently far from energetic equilibrium: but despite this flux, there may be pattern stability, see synergetics. ;Complex systems may exhibit critical transitions :Critical transitions are abrupt shifts in the state of ecosystems, the climate, financial and economic systems or other complex systems that may occur when changing conditions pass a critical or bifurcation point. The 'direction of critical slowing down' in a system's state space may be indicative of a system's future state after such transitions when delayed negative feedbacks leading to oscillatory or other complex dynamics are weak. This structure promotes indirect facilitation and a system's capacity to persist under increasingly harsh circumstances as well as the potential for large-scale systemic regime shifts. ;Dynamic network of multiplicity :As well as coupling rules, the dynamic network of a complex system is important. Small-world or scale-free networks which have many local interactions and a smaller number of inter-area connections are often employed. Natural complex systems often exhibit such topologies. In the human cortex for example, we see dense local connectivity and a few very long axon projections between regions inside the cortex and to other brain regions. Glider Gun creating "gliders" in the cellular automaton Conway's Game of Life ; May produce emergent phenomena :Complex systems may exhibit behaviors that are emergent, which is to say that while the results may be sufficiently determined by the activity of the systems' basic constituents, they may have properties that can only be studied at a higher level. For example, empirical food webs display regular, scale-invariant features across aquatic and terrestrial ecosystems when studied at the level of clustered 'trophic' species. Another example is offered by the termites in a mound which have physiology, biochemistry and biological development at one level of analysis, whereas their social behavior and mound building is a property that emerges from the collection of termites and needs to be analyzed at a different level. ; Relationships are non-linear : In practical terms, this means a small perturbation may cause a large effect (see butterfly effect), a proportional effect, or even no effect at all. In linear systems, the effect is always directly proportional to cause. See nonlinearity. ; Relationships contain feedback loops :Both negative (damping) and positive (amplifying) feedback are always found in complex systems. The effects of an element's behavior are fed back in such a way that the element itself is altered. == 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 (ECI), 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 (RQCI) 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 (i.e. regular) to turbulent (i.e. chaotic) 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. Complexity and education Focusing on issues of student persistence with their studies, Forsman, Moll and Linder explore the "viability of using complexity science as a frame to extend methodological applications for physics education research", finding that "framing a social network analysis within a complexity science perspective offers a new and powerful applicability across a broad range of PER topics". Complexity in healthcare research and practice Healthcare systems are prime examples of complex systems, characterized by interactions among diverse stakeholders, such as patients, providers, policymakers, and researchers, across various sectors like health, government, community, and education. These systems demonstrate properties like non-linearity, emergence, adaptation, and feedback loops. Complexity science in healthcare frames knowledge translation as a dynamic and interconnected network of processes—problem identification, knowledge creation, synthesis, implementation, and evaluation—rather than a linear or cyclical sequence. Such approaches emphasize the importance of understanding and leveraging the interactions within and between these processes and stakeholders to optimize the creation and movement of knowledge. By acknowledging the complex, adaptive nature of healthcare systems, complexity science advocates for continuous stakeholder engagement, transdisciplinary collaboration, and flexible strategies to effectively translate research into practice. Chaotic systems remain deterministic, though their long-term behavior can be difficult to predict with any accuracy. With perfect knowledge of the initial conditions and the relevant equations describing the chaotic system's behavior, one can theoretically make perfectly accurate predictions of the system, though in practice this is impossible to do with arbitrary accuracy. The emergence of complex systems theory shows a domain between deterministic order and randomness which is complex. This is referred to as the "edge of chaos". When one analyzes complex systems, sensitivity to initial conditions, for example, is not an issue as important as it is within chaos theory, in which it prevails. As stated by Colander, the study of complexity is the opposite of the study of chaos. Complexity is about how a huge number of extremely complicated and dynamic sets of relationships can generate some simple behavioral patterns, whereas chaotic behavior, in the sense of deterministic chaos, is the result of a relatively small number of non-linear interactions. who discussed Android's market position, Orlando who explained the corporate dynamics in terms of mutual synchronization and chaos regularization of bursts in a group of chaotically bursting cells and Orlando et al. who modelled financial data (Financial Stress Index, swap and equity, emerging and developed, corporate and government, short and long maturity) with a low-dimensional deterministic model. Therefore, the main difference between chaotic systems and complex systems is their history. Chaotic systems do not rely on their history as complex ones do. Chaotic behavior pushes a system in equilibrium into chaotic order, which means, in other words, out of what we traditionally define as 'order'. On the other hand, complex systems evolve far from equilibrium at the edge of chaos. They evolve at a critical state built up by a history of irreversible and unexpected events, which physicist Murray Gell-Mann called "an accumulation of frozen accidents". In a sense chaotic systems can be regarded as a subset of complex systems distinguished precisely by this absence of historical dependence. Many real complex systems are, in practice and over long but finite periods, robust. However, they do possess the potential for radical qualitative change of kind whilst retaining systemic integrity. Metamorphosis serves as perhaps more than a metaphor for such transformations. Complexity and network science A complex system is usually composed of many components and their interactions. Such a system can be represented by a network where nodes represent the components and links represent their interactions. For example, the Internet can be represented as a network composed of nodes (computers) and links (direct connections between computers). Other examples of complex networks include social networks, financial institution interdependencies, airline networks, and biological networks. == Notable scholars ==