Search results
Results from the WOW.Com Content Network
In mathematics, a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane. Each set of initial conditions is represented by a different point or curve. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in the phase space.
Anyway, using the homotopy analysis method or harmonic balance, one can derive a frequency response equation in the following form: [9] [5] [() + ()] =. For the parameters of the Duffing equation, the above algebraic equation gives the steady state oscillation amplitude z {\displaystyle z} at a given excitation frequency.
In mathematics, a phase portrait is a geometric representation of the orbits of a dynamical system in the phase plane. Each set of initial conditions is represented by a different point or curve. Phase portraits are an invaluable tool in studying dynamical systems. They consist of a plot of typical trajectories in
Plot of the Duffing map showing chaotic behavior, where a = 2.75 and b = 0.15. Phase portrait of a two-well Duffing oscillator (a differential equation, rather than a map) showing chaotic behavior. The Duffing map (also called as 'Holmes map') is a discrete-time dynamical system. It is an example of a dynamical system that exhibits chaotic behavior
In applied mathematics, in particular the context of nonlinear system analysis, a phase plane is a visual display of certain characteristics of certain kinds of differential equations; a coordinate plane with axes being the values of the two state variables, say (x, y), or (q, p) etc. (any pair of variables).
The simplest phase diagrams are pressure–temperature diagrams of a single simple substance, such as water. The axes correspond to the pressure and temperature. The phase diagram shows, in pressure–temperature space, the lines of equilibrium or phase boundaries between the three phases of solid, liquid, and gas.
Related: The 26 Funniest NYT Connections Game Memes You'll Appreciate if You Do This Daily Word Puzzle. Hints About Today's NYT Connections Categories on Monday, January 13. 1. To impart skills ...
Phase portrait showing saddle-node bifurcation. Bifurcation theory is the mathematical study of changes in the qualitative or topological structure of a given family of curves, such as the integral curves of a family of vector fields, and the solutions of a family of differential equations.