Term

Definition

Attractor

A delimited area of space in which a system’s dynamics may or may not move. Common types of attractors include fixed point, limit cycle (periodic), torus (non-periodic), and chaotic.

Bifurcation

A
pattern of instability in which a system achieves greater complexity by
shifting into new forms of dynamical states – e.g., the dynamics of a
system might switch suddenly from a fixed point attractor to a torus or
a chaotic attractor.

Complex System

A
system or network of “simpler” parts that undergo

multiple, iterative interactions between the different components,
influenced additionally by interactions with the system’s own larger
environment (of which the system itself is one part).

Dynamics

The pattern of change or growth of an object or phenomenon. System
dynamics can converge on an attractor pattern , i.e., a group of related
states in phase space bounding the ways in which the system trajectory
recurrently moves. (cf., rigid dynamics associated with fixed point or
limit cycle attractors versus flexible dynamics of Lorenze-type
attractors in person-level and interpersonal behaviors and physiology).

Emergent Properties

A
characteristic of complex systems in which the properties (behaviors) of
the whole are not predicted by the properties (behaviors) of the
individual parts.

Entropy

Also referred to as turbulence, i.e., in motion of water or air (cf.
succussion as a source of turbulence in preparation of homeopathic
remedies). In dynamical systems research, information generated at a
given point in time is used to predict the state of the system at a
later point in time. If the information is lost at a higher rate,
entropy is higher, and vice versa. Higher entropy can mean the system is
moving closer to a chaotic attractor; lower entropy can mean the system
is moving closer to order. The Lyapunov exponent in NDS indicates the
degree of sensitivity to initial conditions of a system, where a
positive value suggests expansion toward chaos and a negative value
suggests contraction toward order (e.g., fixed point or limit cycle
attractor).

Fitness Landscape

An environmental or ecologic niche in which a system (e.g., animal or
plant species) lives and survives with specific adaptations shaped by the environment. Ecological changes force new adaptations and evolution to maintain survival and avoid extinction.

Network

An interconnected, interdependent, interactive system of parts or
people, in which the points of connection are called nodes. The most
highly interconnected nodes (hence most influential within the network)
are hubs. Networks are embedded within other larger networks and are
comprised of smaller networks. For instance, a person is an indivisible
network comprised of organs, but a person is also part of a larger
social network. An organ like the brain is comprised of neurons forming
neural networks. The meridian system of Chinese medicine is a type of
network with hubs and nodes at acupuncture points.

Non-Linearity

A property of systems in which the output is disproportionate in magnitude to the input, a characteristic of complex living systems.

Phase Transition

Qualitative large change in a system because of a small quantitative change in a parameter of the system (cf., unstuckness leading to clinical transformation or relapse).

Self-Organization

The spontaneous self-generated development of a pattern or structure from an unordered dynamical system (cf., patterns of hierarchical change in the course of constitutional treatment, esp. in homeopathy).

Self-Similarity

The characteristic of certain natural geometric forms (e.g,. fractals) or dynamical patterns that exhibit features that appear similar at different levels of scale.

Self-Similarity across levels of scale enables complexity researchers to use findings at one level to inform research designs at higher or lower levels of organizational scale.

Synergetics

The study of nonlinear dynamics in interacting systems. At a given level of entropy in the system, hierarchical driver-slave relationships develop. Drivers in the upper level can control the dynamics of the lower level.

System

A group of independent but interrelated elements comprising a unified whole and interacting with the environment.