Having existed as a term since antiquity, complexity as an idea and scientific concept that definitely necessitates the understanding of origin of complex components, entails lengthy and meticulous computations as well as causal processes [Karaca, Y. (2022)]. From brain network to different species, immune system, economy, among many others, are set as excellent examples of complex systems. For instance, ants are simple organisms, but when they come together in millions, they attain a sort of collective intelligence. Correspondingly, brains like ant colonies possess billions of neurons like ants that work in parallel with no central control. The ontological meaning of information processing shows an integral component of reality. The living systems and their description in biology have become extensively-employed among the information processing networks which also play a prominent role in natural systems such as cellular metabolism, species, immune system, and so on.
The idea of complexity is a unifying framework for science and a component for transformative way of thinking so that the understanding of complex systems can be understood. With behaviors and patterns that are challenging for predicting and controlling complexity and complex systems are applicable to encompass a broad array of phenomena on all scales imaginable. The evolution dynamical systems complexity entails the nature the perspective provided by complexity ensures the identification of forms as well as evolutive characteristics which have to do with all or almost all the systems that constitute a huge number of elements which show reciprocity in interactions, nonlinear interfaces and positive feedback mechanisms within the systems [Karaca, Y. (2022)].
Considering all these factors, they are named complex systems, and the insights from chaos theory and nonlinear mathematics into systems science spur the development of complexity theory. Characterized by unpredictability, uncontrollability and interconnectedness as some of the key elements of complex dynamic systems, the aim of science is directed to better understanding the dynamics and relationships of the systems. The tradeoff between efficiency and adaptability can foster the shift to the aim of science so that the requirement of matching the complexity systems can be fulfilled considering the entailments of their environments on multistage analyses on different scales as well as the evolutionary processes over the due course of time.
The science of complex systems provides us with the methodological and conceptual means in order that issues pertaining to self-organization, emergence and transformation can be tackled by explaining the mechanisms of microlevels and macrolevels based on their patterns and behaviors over time. Some of the characteristics of complex systems include emergence, self-organization, evolution, adaptation, pattern formation, chaos, competition, dynamic responses, scaling, attractors, interdependence, function, cooperation, networks, and so forth. The essential components of complex systems and corresponsive mathematical models as well as simulation strategies along with cellular automata, agent-based modeling, systems representation, statistical methods, informatics and pattern recognition processes have their applications with respect to biological, natural, neurological, cellular, physiological, physical, dynamic, social and psychosocial systems, to cite some. Darwin saw the path to the evolution of complexity, with the varied traits of the species observed in each generation; as new variations emergence and spread come to mean the production of complex structures. Although some of the variations contributed to the increase in their survival, some enabled them to produce more offspring. The organisms which are well-adapted to their environment are more likely to survive and reproduce, passing those advantageous traits to their offspring. Darwin’s answer to the sources of order appeals to one force, which is natural selection in which evolution means gradual changes in the genetic composition of populations over time. Yet, the mingling of self-ordering with these mechanisms unfolds the underlying patterns and makes the order sensible despite the organisms’ complexity. The current landscape of science manifests molecular biology leading to the inmost ultimate mechanisms, complexity and evolution capacity of cells revealing the powers of self-organization [Karaca, Y. (2022)]. The selection ensures that organisms adapt successfully in a co-evolutionary process through organisms whose selection operates on complex co-evolving systems. In addition, pattern formation refers to the organization of structures or cells during development to form specific arrangements. In brief, evolution has an impact on shaping diversity of life, adaptation enables survival. In self-organization, some form of overall order emerges from local interactions between parts of a system disordered initially, and eventually, pattern formation modulates the subtle arrangements of simple units of life as well as cells and tissues at different stages.
Given these considerations and key characteristics, complexity has a broad range of areas in different fields, whereas complexity science is concerned with the tackling of emergence, self-organization, chaos theory, embodied cognitive science, systems theory as well as cybernetics. On this spectrum, Artificial Intelligence (AI) handles the computing in all sorts, including autonomy, digital ecosystems besides the systems of engineering, to name just some. Delving into complex networks considered to offer promising approaches for the modeling of complex systems is involved in different areas generating robust results. In addition, illustrative examples, case studies, applications, simulations, to address some, for each respective field can ensure tools for the identification of relevant structures in various spaces of complex systems allowing the optimal characterization of complex networks, while bearing in mind the importance of considering the constitutive parts of the underlying system by contemplating on a complex system’s modeling.
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