Long Tail Distributions


Long Tail Distributions A long tail distribution is one that has very few occurrences of very large events, and very many occurrences of very small events, which gives the graph a "long tail." This "long tail" is generated by a power law relationship, meaning there is a power relationship between the size of an event [...]

Long Tail Distributions 2019-01-11T14:03:59+00:00

Exponents & Power Laws


Exponents & Power Laws The term power law describes a functional relationship between two quantities, where one quantity varies as a power - or exponent - of another.View Source Part of the definition to linear systems is that the relationship between input and output is related in a linear fashion. The ratio of input [...]

Exponents & Power Laws 2019-01-11T14:05:08+00:00



Fractals Fractals are both physical phenomenon and mathematical objects, exhibiting a repeating pattern that is displayed at various levels of magnitude, what is called scale invariance, creating self-similar patterns under magnification.View Source Fractals are sometimes called the pictures of nature, and if chaos theory, as the name implies, is the chaotic and unpredictable dimension [...]

Fractals 2019-01-11T14:05:38+00:00

Phase Transitions


Phase Transitions Phase transitions and bifurcations are periods of qualitative and often rapid change in the dynamics of a nonlinear system’s state.View Source They involve positive feedback loops that drive the system far-from-equilibrium and result in exponential change and a pattern of development called punctuated equilibrium where periods of stability are punctuated by phases [...]

Phase Transitions 2019-01-11T14:05:44+00:00

Butterfly Effect


Butterfly Effect The butterfly effect is a popular term for what is called sensitive dependence on initial conditions in which a small change in some input state to a nonlinear system can result in a vastly disproportionate output at a later stage.View Source The term is thought to derive from the title of a [...]

Butterfly Effect 2019-01-11T14:05:48+00:00

Nonlinear Dynamics & Chaos


Nonlinear Dynamics & Chaos Chaos theory is the study of nonlinear systems dynamics whose development is marked by iteration and feedback loops, making them sensitive to initial conditions (what is called the butterfly effect). Even though these nonlinear systems may be deterministic, such as a double pendulum, their long-term trajectory is typically not possible to [...]

Nonlinear Dynamics & Chaos 2019-01-11T14:05:59+00:00

Dynamical Systems


Dynamical Systems Within science and mathematics, dynamics is the study of how things change with respect to time. As opposed to describing things simply in terms of their static properties, the patterns we observe all around us in how the state of things changes over time is an alternative way through which we can describe [...]

Dynamical Systems 2019-01-11T14:06:13+00:00

Mean Field Theory


Mean Field Theory Mean field theory comes from the domain of physics and in particular statistical mechanics where researchers are dealing with many interacting variables, such as gas molecules in a chamber. The main idea of mean field theory is to replace all interactions to any one body with an average interaction. This reduces any [...]

Mean Field Theory 2019-01-11T14:15:21+00:00

Tipping Points


Tipping Points The term "tipping point" in its most basic meaning refers to a critical point when unprecedented changes occur rapidly with irreversible effect.View Source A tipping point is understood as a point in time when a group of agents—or a large number of group members—rapidly and dramatically changes its behavior by widely adopting a [...]

Tipping Points 2018-06-22T20:54:27+00:00