The Concept of Nonlinearity in Complex Systems

Abstract

Background: Nonlinear systems are found everywhere throughout the natural world. In these systems there exists no proportionality and no simple causality between the magnitude of responses and the strength of their stimuli: small changes can have striking and unanticipated effects, whereas great stimuli will not always lead to drastic changes in a system's behavior. Over the past few years, several groups have been interested in pursuing the relevance of nonlinear concepts to medicine. Although the initial focus was on cardiovascular and neurophysiologic dynamics, it soon became clear that the models they were using had more general applications in biology and medicine. In the field of traumatology, up to now the nonlinear dynamics of the innumerable reactions and feedback loops at many structural levels of the traumatized patient have not been analyzed. Method: For a better understanding of the concept of nonlinearity and its possible implications in the field of traumatology, three examples at the molecular, the cellular and the organic levels are presented. Results and Conclusions: Nonlinear behavior in principle is the rule in highly complex reactions. This nonlinearity exists also in traumatologically relevant systems. The theories of nonlinear dynamics offer new mathematical tools to quantify, model, predict or modulate the behavior of biological systems. It should be demonstrated that the traditional Newtonian linear approach and the new nonlinear approach are essential dual aspects of any system, both being essential for a better understanding of the pathophysiologic reactions in complex situations like trauma, shock, and sepsis.

Computational Methods for Single-Cell Imaging and Omics Data Integration

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Hybridity, Adaptive Peacebuilding and Complexity

“…Non-linearity in relational mechanisms in complex systems means that small, localised disturbances can evolve into critical states that impact the entire system (Bak 1999). As such, the system will have properties, and exhibit behaviours or mechanisms that cannot be analysed or traced through an analysis of its elements (Willy et al 2003). If an alien were to observe humans they may observe men, women and children, and some of their relationships, but they will not be able to easily identify the invisible emergent and self-organising cultural processes that organise them into families, clans and societies.…”

“…Whereas complicated systems-for example an advanced aircraft or super-computer-can be comprehensively described and understood through an observation and analysis of their components and how they work together to produce a specific effect, a system that is complex cannot be understood via an analysis of its constituent elements (Cilliers 1998). In contrast to linear complicated systems, a complex system output is more than just the sum of inputs (Willy et al 2003). Non-linearity in relational mechanisms in complex systems means that small, localised disturbances can evolve into critical states that impact the entire system (Bak 1999).…”

The Inadequacy of Classical Regulatory Approaches in a Complex Environment

“…3 Interdependence becomes dynamic when over time two or more agents interact and produce changes based on their interaction. 4 And in the dynamic, complex networks the rule is nonlinear behaviour (Willy et al, 2003), where the law changes concerning the scale of variables (parameters) and as such is the distortion of the linear graph or the proportionality relation. (Yoshida, 2010) When people connect, the elements of complexity can be found in the nonlinearity, communication, emergence, diversity and prediction.…”