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Complexity theory refers to the study of the behavior of complex systems. A complex system is a system (whole) composed of numerous interacting entities (parts), each of which is behaving in its local context according to some rule(s) or force(s). Complexity theory is a new field of science interested in understanding how parts of a system give rise to its collective behavior, how collective behavior affects its parts, and how systems interact with their environment. Its focus on questions about parts, wholes, and relationships are relevant to many fields of science such as physics, biology, medicine, economics, and organization studies. Across a number of different fields of study, it has been shown that complex systems are subject to common patterns of behavior. This finding has led to a remarkable development of the study of complex systems in the last two decades. The goal of complexity theory as a discipline is to understand the properties of different kinds of complex systems such as the brain, stock markets, the weather, families, corporations, molecules, and so forth.

Conceptual Overview

The Origins

Before the current wave of interest in complexity and complex systems that constitutes the core of this work, there have been two previous waves of interest in complexity and complex systems. The first wave took place in Europe after World War I, giving birth to the term holism and to interest in gestalt theories. Holism regards natural objects as wholes that are not entirely resolvable into parts, that are more than the sum of their parts, and the mechanical act of putting together their parts will not produce them or account for their characters and behavior. Applied to complex systems, holism postulates new properties and relationships among subsystems that had no place in the system components: hence it calls for emergence.

The second wave can be tracked to during and just after World War II with the emergence of cybernetics and general systems theory. Cybernetics focused on the coordination, regulation, and control of systems by feedback loops. Cybernetics had two key drivers: (1) the search for a goal (or standard) oriented toward a particular objective, and (2) the need for adaptation to the environment. These drivers allowed the use of strategic planning to define the plan to get the goal, to set the control systems, and to use (negative) feedback systems to adapt to changes in the environment to keep the system moving toward the goal.

General Systems Theory

General systems theory focused on the understanding of the deep principles underlying all types of systems whose components are linked by feedback loops. These theories gave rise to the growth of the systems design school in organization theory and the development of system dynamics whose models inform a broad stream of research in the study of nonlinear complex patterns of behavior.

Catastrophe Theory

The third or current wave of theories in the study of complex systems emerged at the end of the 1960s. Catastrophe theory appeared on the scene by 1968. It is a solid body of mathematics that classifies nonlinear dynamic systems according to their modes of behavior. Catastrophic events occur in a system when a small shift in a parameter of a deterministic system could send the system from one equilibrium to another (for instance, from static equilibrium to periodic cycles) or to an unstable state in which variables increase without limit. A feedback loop that does not operate in a limiting way (negative feedback) but, instead, escalates small changes generating amplified fluctuations of a very unstable kind is called positive feedback.

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