Order of magnitudeAn order of magnitude is an approximation of the logarithm of a value relative to some contextually understood reference value, usually 10, interpreted as the base of the logarithm and the representative of values of magnitude one. Logarithmic distributions are common in nature and considering the order of magnitude of values sampled from such a distribution can be more intuitive. When the reference value is 10, the order of magnitude can be understood as the number of digits in the base-10 representation of the value.
Sociotechnical systemSociotechnical systems (STS) in organizational development is an approach to complex organizational work design that recognizes the interaction between people and technology in workplaces. The term also refers to coherent systems of human relations, technical objects, and cybernetic processes that inhere to large, complex infrastructures. Social society, and its constituent substructures, qualify as complex sociotechnical systems.
PredictabilityPredictability is the degree to which a correct prediction or forecast of a system's state can be made, either qualitatively or quantitatively. Causal determinism has a strong relationship with predictability. Perfect predictability implies strict determinism, but lack of predictability does not necessarily imply lack of determinism. Limitations on predictability could be caused by factors such as a lack of information or excessive complexity. In experimental physics, there are always observational errors determining variables such as positions and velocities.
TransdisciplinarityTransdisciplinarity connotes a research strategy that crosses many disciplinary boundaries to create a holistic approach. It applies to research efforts focused on problems that cross the boundaries of two or more disciplines, such as research on effective information systems for biomedical research (see bioinformatics), and can refer to concepts or methods that were originally developed by one discipline, but are now used by several others, such as ethnography, a field research method originally developed in anthropology but now widely used by other disciplines.
Gibbs measureIn mathematics, the Gibbs measure, named after Josiah Willard Gibbs, is a probability measure frequently seen in many problems of probability theory and statistical mechanics. It is a generalization of the canonical ensemble to infinite systems. The canonical ensemble gives the probability of the system X being in state x (equivalently, of the random variable X having value x) as Here, E is a function from the space of states to the real numbers; in physics applications, E(x) is interpreted as the energy of the configuration x.
Linear stabilityIn mathematics, in the theory of differential equations and dynamical systems, a particular stationary or quasistationary solution to a nonlinear system is called linearly unstable if the linearization of the equation at this solution has the form , where r is the perturbation to the steady state, A is a linear operator whose spectrum contains eigenvalues with positive real part. If all the eigenvalues have negative real part, then the solution is called linearly stable.
Homoclinic orbitIn the study of dynamical systems, a homoclinic orbit is a path through phase space which joins a saddle equilibrium point to itself. More precisely, a homoclinic orbit lies in the intersection of the stable manifold and the unstable manifold of an equilibrium. It is a heteroclinic orbit–a path between any two equilibrium points–in which the endpoints are one and the same.
Heteroclinic orbit[[Image:Heteroclinic orbit in pendulum phaseportrait.png|thumb|right|The phase portrait of the pendulum equation math|1=''x + sin x = 0. The highlighted curve shows the heteroclinic orbit from (x, x′) = (–π, 0) to (x, x′) = (π, 0). This orbit corresponds with the (rigid) pendulum starting upright, making one revolution through its lowest position, and ending upright again.]] In mathematics, in the phase portrait of a dynamical system, a heteroclinic orbit (sometimes called a heteroclinic connection) is a path in phase space which joins two different equilibrium points.
Catastrophe theoryIn mathematics, catastrophe theory is a branch of bifurcation theory in the study of dynamical systems; it is also a particular special case of more general singularity theory in geometry. Bifurcation theory studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances, analysing how the qualitative nature of equation solutions depends on the parameters that appear in the equation. This may lead to sudden and dramatic changes, for example the unpredictable timing and magnitude of a landslide.
IntermittencyIn dynamical systems, intermittency is the irregular alternation of phases of apparently periodic and chaotic dynamics (Pomeau–Manneville dynamics), or different forms of chaotic dynamics (crisis-induced intermittency). Experimentally, intermittency appears as long periods of almost periodic behavior interrupted by chaotic behavior. As control variables change, the chaotic behavior become more frequent until the system is fully chaotic. This progression is known as the intermittency route to chaos.
