Área de Física Teórica de la Universidad de Extremadura

       Asignatura: Métodos de la Física Matemática

Curso: 3º de la Licenciatura de Física 

ProfesoresSantos Bravo Yuste y Vicente Garzó Puertos

Some didactic resources


Phase Portrait and Field Directions of Two-Dimensional Linear Systems of ODEs

This Demonstration plots the phase portrait (or phase plane) and the vector field of directions around the fixed point (0,0) of the two-dimensional linear system of first-order ordinary differential equations

dx/dt = a1 x + b1 y

dy/dt = a2 x + b2 y

Drag the four locators (the big circles) to see the trajectories of four solutions of the system that go through them. The position of these points can be chosen by clicking on wherever you like inside the graphics. Thick orange lines parallel to the eigenvectors are shown if the eigenvalues of the system are real


Phase portrait  and  vector field of directions of  some nonlinear first-order differential equations

You can study (and play with) the phase portrait (or phase plane) and the vector field of directions of the systems 

of the book "Métodos Mátemáticos Avanzados para Científicos e Ingenieros" by means of the Mathematica notebooks that you can download from the corresponding hyperlinks.

For using these notebooks you need Mathematica 7 or the Mathematica Player program (which can be downloaded from http://www.wolfram.com/products/player/.) You can choose the region of the phase plane where the solutions and vector field of directions are shown, and, also, the values of the parameters "a" and " b" that describe the actual system.  Trajectories of several solutions of the system that go through the "locators" (the big circles) are shown. The position of these locators can be chosen by clicking on wherever you like inside the graphics, or, simply, by dragging them to the location you like.


Phase portrait  and  vector field of directions of  the Lotka-Volterra equations

You can study (and play with) the phase portrait (or phase plane) and the vector field of directions of the Lotka-Volterra equations given in the

of the book "Métodos Mátemáticos Avanzados para Científicos e Ingenieros" by means of the Mathematica notebook that you can download from the previous hyperlink.

For using this notebook you need Mathematica 7 or the Mathematica Player program (which can be downloaded from http://www.wolfram.com/products/player/.)  You can choose the region of the phase plane where the solutions and vector field of directions are shown, and, also, the values of the parameters "a" , " b" , "α" and "β" that describe the actual system.  Trajectories of several solutions of the system that go through the "locators" (the big circles) are shown. The position of these locators can be chosen by clicking on wherever you like inside the graphics, or, simply, by dragging them to the location you like.