Plotting, NDSolve, initial conditions from range, inequalities [closed]

I will do my best to describe the simplest version of my problem as clearly as I can. Please bear with me:

We have a,b and c which are functions of x and y, and their t-evolution is given by coupled non-linear differential equations in {expr}. I have:

NDSolve[{expr},a==A,b==B,c==C,{a,b,c},{t,0,10}]

Now I want to essentially plot y vs x, displaying the band of values for which:

• a<1 for all t in range.
• with the initial conditions a,b,c specified by a range in x and in y -- the axes of the plot. Am confused about the syntax for this.

Essentially I am trying to plot, on an x-y plot, the band of values for which certain functions of them, a,b,c, with DE's giving their time evolution, satisfy a certain inequality for all t in a range.

Additionally, would be great if I was also able to plot this 3D region:

• run t to infinity and plot on an x-y plot the cutoff t value where the inequality condition ceases to hold, on the z axis, and

• same thing but plot on the z axis the value for which t is singular (I know there exists a pole at large t)

Work so far (Note, the evolutions depend on a very large set of very complex DE's, so I have omitted them for simplicity):

• Poles: When I simply do NDSolve[{expr},{a,b,c},{t,0,100}] with a set of chosen initial conditions in {expr}, it gives me the pole for this set, i.e. "At t==20.3256 step size is effectively zero; singularity or stiff system suspected." Wondering how to automate this and have variable initial conditions and store all the singularities. That would allow me to plot x,y,t-pole values. Confused about the syntax of making variable initial conditions (in terms of x,y) and where to specify a,b,c in terms of x,y.

• Plots: Again by choosing particular initial condition values I am able to use NDSolveValue to extract the a,b,c values as functions of t and plot their t behaviour. Alas, this is not the eventual plot I want -- I have to somehow check for my inequality conditions at every point in his plot and plot the a,b,c values that satisfy the conditions as regions on an x,y plot.

• Cutoff: Once again with specified initial values I can use a WhenEvent[a[t]=1,Print[t]]},a,{t,0,100}] function to output the cutoff value where the inequality a<1 stops being true. Not sure how to implement such a function with the initial values in the NDSolve scanning through a range.

I'm very new to Mathematica so would appreciate any help or guidance.

closed as off-topic by m_goldberg, Sektor, halirutan♦, Coolwater, Henrik SchumacherMay 28 '18 at 7:39

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question cannot be answered without additional information. Questions on problems in code must describe the specific problem and include valid code to reproduce it. Any data used for programming examples should be embedded in the question or code to generate the (fake) data must be included." – m_goldberg, Sektor, halirutan, Coolwater, Henrik Schumacher
If this question can be reworded to fit the rules in the help center, please edit the question.

• I don't think we can help you without knowing what your differential equations are. – m_goldberg May 27 '18 at 15:55
• Welcome to StackExchange. As m_goldberg already said, your question would be really hard to answer without an example. In addition to that, your question contains many sub-questions. Usually, such questions won't get as much attention as they could get when you would concentrate on one problem per question. – halirutan May 27 '18 at 16:06
• @m_goldberg - Thanks, I will try reword this – SarahThompson May 28 '18 at 1:51
• @halirutan - Thank you. I will take your advice and write sub-questions. What's the etiquette for closing a question, so that I may write a new one? – SarahThompson May 28 '18 at 1:52
• @halirutan - After simplifying my problem I have rewritten it in another question: mathematica.stackexchange.com/questions/174089/… – SarahThompson May 28 '18 at 1:58