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An important question in terms of dynamical systems is how the behavior of the trajectory changes when the parameter r changes. Depending on the value of r, the behavior of the trajectory of the logistic map can be simple or complex. [Thompson & Stewart 1] Below, we will explain how the behavior of the logistic map changes as r increases.
Control charts are graphical plots used in production control to determine whether quality and manufacturing processes are being controlled under stable conditions. (ISO 7870-1) [1] The hourly status is arranged on the graph, and the occurrence of abnormalities is judged based on the presence of data that differs from the conventional trend or deviates from the control limit line.
The above line diagram consists of circles, connecting line segments, and labels. Circles represent formal concepts. The lines allow to read off the subconcept-superconcept hierarchy. Each object and attribute name is used as a label exactly once in the diagram, with objects below and attributes above concept circles.
The figure shows the schematic P-T diagram of a pure substance (as opposed to mixtures, which have additional state variables and richer phase diagrams, discussed below). The commonly known phases solid , liquid and vapor are separated by phase boundaries, i.e. pressure–temperature combinations where two phases can coexist.
A typical phase diagram.The solid green line applies to most substances; the dashed green line gives the anomalous behavior of water. In thermodynamics, the triple point of a substance is the temperature and pressure at which the three phases (gas, liquid, and solid) of that substance coexist in thermodynamic equilibrium. [1]
A line, usually vertical, represents an interval of the domain of the derivative.The critical points (i.e., roots of the derivative , points such that () =) are indicated, and the intervals between the critical points have their signs indicated with arrows: an interval over which the derivative is positive has an arrow pointing in the positive direction along the line (up or right), and an ...
Symmetry breaking in pitchfork bifurcation as the parameter ε is varied. ε = 0 is the case of symmetric pitchfork bifurcation.. In a dynamical system such as ¨ + (;) + =, which is structurally stable when , if a bifurcation diagram is plotted, treating as the bifurcation parameter, but for different values of , the case = is the symmetric pitchfork bifurcation.
A particularly important instance arises in toxicology, where the model for the effect of a drug may be that there is zero effect for a dose below a critical or threshold value, while an effect of some significance exists above that value. [1] Certain types of regression model may include threshold effects. [1]