Exponents & Power Laws

2019-01-11T14:05:08+00:00

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 Laws2019-01-11T14:05:08+00:00

Fractals

2019-01-11T14:05:38+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 [...]

Fractals2019-01-11T14:05:38+00:00

Phase Transitions

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

Phase Transitions Phase transitions and bifurcations are periods of qualitative and often rapid change in the dynamics of a nonlinear systemâ€™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 Transitions2019-01-11T14:05:44+00:00

Butterfly Effect

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

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 Effect2019-01-11T14:05:48+00:00

Nonlinear Dynamics & Chaos

2019-01-11T14:05:59+00:00

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 & Chaos2019-01-11T14:05:59+00:00

Dynamical Systems

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

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 Systems2019-01-11T14:06:13+00:00