Edgeware- Glossary

Benard System:

A simple physical system, consisting of a certain liquid in a container being heated from the bottom, which has been extensively studied by the Prigogine School because it demonstrates self-organization and emergence. As the liquid in a container is heated from the bottom, at a critical temperature level (a far-from-equilibrium condition), there is the sudden emergence of striking hexagonally-shaped convection cells. Prigogine has termed these hexagonal cells "dissipative structures" since they maintain their structure while dissipating energy through the system and from the system to the environment. These "dissipative structures" are a good example of unpredictable emergent patterns since the direction of rotation of the convection cells is the result of the amplification of random currents in the liquid.

See: Dissipative Structures; Emergence; Far-from-equilibrium; Self-organization

Bibliography: Prigogine and Stengers (1984); Goldstein (1994).

List of Terms

Bifurcation:

The emergence of a new attractor(s) in a dynamical, complex system that occurs when some parameter reaches a critical level (a far-from-equilibrium condition). For example in the logistic equation or map system, bifurcation and the emergence of new attractors take place when the parameter representing birth/death rates in a population reaches a critical value. More generally, a bifurcation is when a system shows an abrupt change in typical behavior or functioning that lasts over time. For example, a change of an organizational policy or practice which results in a long-term change of the business’ or institution’s behavior can be considered a bifurcation.

See: Attractor; Dynamical System; Far-from-equilibrium; Logistic Equation

Bibliography: Abraham, et. al. (1991); Guastello (1995).

List of Terms

Boundaries (Containers):

Processes of self-organization and emergence occur within bounded regions, e.g., the container holding the Benard System so that the liquid is intact as it undergoes far-from- equilibrium conditions. In cellular automata the container is the electronic network itself which is "wrapped around" in that cells at the outskirts of the field are hooked back into the field. These boundaries or containers act to demarcate a system from its environment, and, thereby, maintain the identity of a system as it changes. Furthermore, boundaries channel the nonlinear processes at work during self-organization. In human systems, boundaries can refer to the actual physical plant, organizational policies, "rules" of interaction, and whatever serves to underlie an organization’s identity and that distinguishes an organization from its boundaries. Boundaries need to be both permeable in the sense that they allow exchange between a system and its environments as well as impermeable in so far as they circumscribe the identity of a system in contrast with its environments.

See: Autopoeisis

Bibliography: Eoyang (1997); Goldstein (1994).

List of Terms

Butterfly Effect:

A popular image portraying the property of sensitive dependence on initial conditions in chaotic systems, i.e., a small change having a huge impact like a butterfly flapping its wings in South America eventually leading to a thunderstorm in North America. Some attribute the term "Butterfly" in "Butterfly Effect" to the butterfly-like shape of the phase portrait of the chaotic attractor discovered by the meteorologist Edward Lorenz when he first discerned in his computer runs what was later termed "chaos." The Butterfly Effect introduces a great amount of unpredictability into a system since one can never have perfect accuracy in determining those present conditions which may be amplified and lead to a drastically different outcome than expected. However, since chaotic attractors are not random but operate within a circumscribed region of phase or state space, there still exists a certain amount of predictability associated with chaotic systems. Thus, a particular state of the weather may be unpredictable more than a few days in advance, nevertheless, climate and season reduce the range of possible states of the weather, thereby, adding some degree of predictability even into chaotic systems.

See: Chaos; Sensitive Dependence on Initial Conditions

Bibliography: Abraham, et. al. (1991); Lorenz (1993); Peak and Frame (1994)