These plots show a parametric function which has a variable phase offset in one component. The phase step size is pi/48. The plot shape changes drastically when the phase offset approaches pi/6. The center plot is the closest approximation to a stable cycle. Stability is relevant to acid-base chemistry, predator-prey dynamics, and ecological resilience to climate change. In atmospheric and plasma dynamics, stability can refer to either a physical environment or a computer simulation. Instabilities in space plasmas may provide a source of energy for waves. Numerical instability in a simulation may indicate that a variable is not properly conserved or that the physical environment is sensitive to perturbations.
The figure below is called a complete graph because each point is connected to all other points. The blue line segments form an approximation of a circle. The points represent data collected at a particular time stamp or within a particular time window. If the blue lines represent the sequential order of points from start to finish, this data interval corresponds to a wave. However, if the green line represents the sequential order of points, the data interval would not correspond to a wave. This figure illustrates the need for time-sensitive data analysis methods when searching for wave intervals.
These plots show two waveforms in each subplot. The purple waveform is the same in every plot. The cyan waveform evolves with a time from left-to-right and phase from top to bottom. The group of narrow oscillations is called a wavepacket. The background wave propagates to the left, and the wavepacket propagates to the right with respect to the background wave. From an observer's point of view, both the wave and wavepacket move towards the left side of the page as time increases. Counter-propagating features appear in Earth's jet stream as Rossby waves and in space plasmas as shock-generated whistler waves.
Perhaps this figure should go with my illustrative diagrams, but I used equations in Mathematica instead of Powerpoint shapes.
