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Phase plane plotter. dx/dt=. dy/dt=. The direction field solver knows about trigonometric, logarithmic and exponential functions, but multiplication and evaluation must be entered explicitly (2*x and sin (x), not 2x and sin x). The Display:
- Direction Field Plotter
Licensing: This web page is provided in hopes that it will...
- Direction Field Plotter
1. Non-linear planar systems. With LCC systems detailed, we now move on to the general non-linear planar system1. x0 = f(x; y); y0 = g(x; y) and, with x = (x; y) and F = (f; g), the vector form. (S) x0 = F(x): The path of a solution in the phase plane is called a solution curve or an orbit.
The locus in the (x1-x2)-plane of the solution x(t)for all t >0is a curve that passes through the point x0. This curve is called a trajectory or orbit of (6) from x0. The (x1-x2)-plane is called state plane or phase plane. Using vector notation x˙ =f(x), (7) where f(x)=(f1(x),f2(x))we consider f(x)as a vector field on the state plane.
To draw the phase plane, we must calculate and plot the nullclines, fill in enough direction-field arrows to see how solutions move through the phase plane, identify steady states and determine their stability graphically (if possible) and plot a few example solution curves.
Phase-Plane Techniques 11.1 Plane Autonomous Systems A plane autonomous system is a pair of simultaneous first-order differential equations, x˙ = f(x,y), y˙ = g(x,y). This system has an equilibrium point (or fixed point or critical point or singular point) (x 0,y 0) when f(x 0,y 0) = g(x 0,y 0) = 0. We can illustrate the behaviour of the ...
PhaPl: Phase Plane Helper. PhaPl is a software to research and plot phase portraits of autonomous systems of 2 differential equations on a plane. PhaPl works as a site or as a local html-page that works offline. Go to task input/choice below. Download archive for local offline use (~9 MB to download, ~37 MB to be stored unpacked on disk).
Phase Plane Diagrams. Jordan Canonical Forms. Example. Conclusion. Dewland, Weston, Weyrens. Phase Plane Diagrams of Difference Equations. Goals. Model discrete dynamical systems to determine outcome. Determine qualitative features of a system of homogeneous difference equations with constant coefficients. System of Difference Equations.
