Linked Questions

6
votes
1answer
3k views

Rosenzweig-MacArthur predator-prey model [duplicate]

The predator-prey model is governed by the following system of ode's. \begin{eqnarray} &&\displaystyle{\frac{dx}{dt}=r x\left(1 - \frac{x}{K}\right) - \frac{s y x}{1 + s \tau x}},\\[0.1cm] &...
2
votes
3answers
4k views

Phase space vector field [duplicate]

I have a system of non linear equations and from NDSolve I get the solution. I plot the phase space with ...
1
vote
1answer
4k views

How can I draw this particular phase diagram in Mathematica? [duplicate]

Sketch the phase diagram for systems with the following velocity functions where a and b are constants with ...
2
votes
1answer
710 views

How to plot Van der Pol equation's limit cycle? [duplicate]

The Van der Pol equation is $$y''-\mu (1-y^2)y'+y=0, \,\, \mbox{where}\,\, \mu ≥ 0. $$ Use the Runge-Kutta Method to plot the limit cycle and some solutions in the phase plane (the $yy'$-plane) ...
528
votes
19answers
132k views

Where can I find examples of good Mathematica programming practice?

I consider myself a pretty good Mathematica programmer, but I'm always looking out for ways to either improve my way of doing things in Mathematica, or to see if there's something nifty that I haven't ...
2
votes
3answers
2k views

Phase portraits and StreamPlot

I typed StreamPlot[{y, x-x^3-0.3y+0.5Cos[1.25t]}, {x, -2.5, 2.5}, {y, -2.5, 2.5}] but all I got was a blank plot. What did I do wrong and can I fix it?
1
vote
4answers
5k views

How do I plot x[t] vs. x'[t] (where x[t] and x'[t] are solutions to NDSolve)?

I have a differential equation which I solved using NDSolve. I can easily plot x[t] vs. t, x'[t] vs. t, but.... how do I plot x[t] vs. x'[t]? I tried using the Evaluate function to simplify things, ...
8
votes
3answers
1k views

How to plot the stable and unstable manifolds of a hyperbolic fixed point of a nonlinear system of differential equations?

Suppose we have the following simplified system of two ordinary differential equations: $$\dot{x}(t)=x(t)^2+2y(t)\\ \dot{y}(t)=3x(t)$$ The system has a hyperbolic fixed point the origin. Hence there ...
4
votes
3answers
918 views

Phase lines, vector fields, and fixed points

The differential equation I am trying to visualize the solution to is $\dot x=\sin x$. We can find the solutions to be $$-\ln|\csc x+\cot x|+C.$$ This result it correct, but hard to visualize. Looking ...
2
votes
2answers
763 views

Plotting geodesics of upper half plane

I want to solve (numerically) the geodesics of the upper half plane and plot. The results are quite known (i) straight lines parallel to $y$-axis and (ii) semicircles centered on the $x$-axis. Now the ...
3
votes
1answer
548 views

Is there a Mathematica version of ODE tools pplane and dfield?

The toolkits dfield and pplane are staples in ODE courses. First in MATLAB, now in Java. Do they have a Mathematica expression? Sample outputs follow: @Michael E2 Your suggestions were great. Here ...
1
vote
1answer
691 views

Plotting simple ODE system phase portrait [duplicate]

I am new to Mathematica, please help me to handle the following problem: I have the following system of equations: \begin{cases} \dot x = 2xy \\ \dot y = 1 - x^2 - y^2 \end{cases} What I want is to ...
0
votes
1answer
499 views

How can I create a phase plane? [duplicate]

I want to make a phase plane for an equation system. I want it to look something like a Mu-Space in Stat-Mech. Basically I want it to show the same system with various different initial condition ...
2
votes
1answer
388 views

Projection of a 3D ODE solution on a parametric 2D streamplot

Problem I have a third-order dynamical system of which I'd like to plot the solutions on the streamplot defined by the same dynamical system, as a function of one of the three variables. These are ...
1
vote
1answer
169 views

Phase portrait plotting

I'm trying to plot a phase portrait for the equation: (d^2/dt^2)y + b * (dy/dt)^2 = A, A > 0, b < 0 The first thing I did was changing ...

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