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Systems Science

Systems in Science Systems Sciences & Complex Systems Nonlinear Systems Dynamic Systems Chaotic Systems Control Systems Medical & Clinical Systems

Chaos, as an epiphenomenon that often goes alongside with complexity, may not always follow from it in all cases given the importance of the interactions concerning different levels of agents that form emergent patterns which rely on complex system-theoretic standpoint. On one hand, the inclination in nature shows different and significant properties of chaotic systems that can be marked by unpredictability, non-periodicity, alterations in state, irregularity, feedback loops initial value sensitivity and ergodicity, among other ones. These intricate relationships manifest the behavior of nonlinear dynamical systems. On the other hand, it is seen that nature escapes the world- weariness of predictability as a result of the varying degrees of interaction on various levels and timescales between chance and choice along with the nonlinearity of the complex systems [Karaca, Y. (2022)]. Such variations and far-reaching conditions like feedback, non-linearity, spontaneous order, robustness, lack of central control, hierarchical organization as well as emergence are exposed in complexity that reveals different deep and intricate layers. The large number of complex independent interacting components with mechanisms working in concert and multiple pathways by which the complex system can evolve further point some of the reasons for causality, which is relative and subject to fundamental variations that rely on external factors, perception, complex environment, space and time. Although the term chaos is generally used to refer to disorder or confusion, in science, it is an important conceptual paradox with precise mathematical meaning that says: “a chaotic system is a deterministic system which is difficult to predict.” On the other hand, the definition of a deterministic system is the one whose state at a given one time wholly determines its state for all the future times. The prediction of a deterministic system can be difficult since what happens in the future can be highly sensitive to the current state of the system.

Chaotic systems are systems with behavior being highly sensitive to the initial conditions, and many of the real-world systems can be deemed to be chaotic system. Theory of chaos has applications in diverse areas, which renders parameter identification of chaotic systems a thought-provoking area in system science with schemes developed to attain parameter identification task. These elements also come along with complexity along with openness, non-linearity, chaos, self-organization and synergetics. Across these lines, non-linearity of evolution, chaos, space-time elements and complexity arise as important aspects, which is aptly quoted as: “Our vision of nature is undergoing a radical change toward the multiple, the temporal, and the complex” [Knyazeva, H. (2004)]. It is noted that life requires structural complexity; yet, there is also the chaotic mixture of highly complex organic compounds at stake, which points to the fact that life also requires a specific degree of structural order [Karaca, Y. (2022)].

The handling of chaotic systems is derived from nonlinear system theory, and chaotic systems, as low-dimensional systems, are stated to be unpredictable in spite of being deterministic as the nonlinear interaction among its components excludes detailed analysis and prediction. Complex systems with their many degrees of freedom interacting in complicated ways show that complexity itself can be measured. Although the measurement is possible through number of complexity measures, the mere description or measurement of complexity is not enough to understand complex systems. Emergence in complex systems theory explains the appearance of new qualitative features on the level of the entire systems, while self-organization draws heavily from the related source of qualitative innovation in complex systems. You may refer to...