@janhardo code in simple shape if possible?

@acer but i need another step if possible, i want the outcome be like this picture, i can arange by hand but for being mistakles say S[1]=# and S[2]=# 

Download S.mw

@dharr i have a lot example and the lymic cycle topic contain a lot of phenomena which i will study more on it i have to find the best way for a system have periodic solution or not, i will collecting data more, thank you so much

@dharr  this is first time i saw this, which a system have two different consevation  depend on u and v and  really is so importan but becuase the conservation must contionuios and out conservation is not continious becuase of that the pretty option of plot is not work on it but this is very new for me i have to work on it more, thank you so much it is a very big help 

@dharr i don't have idea to plot polar system like that i have a lot example ,even in some of them we have trapping region 

@Rouben Rostamian  i didn't mention that ODE becuase i say maybe is not related i take  out the ODE  and will upload here,  i am say maybe you are work just with system not PDe-->ODE, i have the whole idea about this topic just i need some help of coding specially in last question about conservation quantity is called first integral i study that, Let me upload program and picture i hope help me more and if i did mistake please modified , please if need anything more tell me, i will work on it more and more

F-ode-Fpaper.mw

@acer is about why not coming out the result is not that 

@Rouben Rostamian  i watch your is so good, but there is some questions appear for me, i am back the problem and try to figure out he give some constant a number but didn't mentioned all, like k,tau, and delta, and i set them 1 but the figure not show me anything

i have to change the problem, in case they didn't mentioned 

mw.mw

@dharr  i didn't have any idea about that untill you explain it, i didn't notice that which we must have that  Conserved quantity

i have to study about that more to get full notion thank you so much

@dharr  @Rouben Rostamian  it is first time i face this How we can calculate this even by hand if lecture exist  please mention it? if we can do phase portrait of system by Conserved quantity so we don't need the jacobian even?  always is times by -1/2?

@Rouben Rostamian  thank you so much , it seems you are a profisional in this topic i am glad to have you here.

@Rouben Rostamian   i didn't know which we can do that by maple, really is so good, i saw a lot of phase portrait with a lot of design is been a while i am searching for finding and plot them this is good really, but the direction of trajectory is missing can we have the direction and point inside the plot are shown?

i saw a lot of phase portrait this is so good and i am looking for this code, and other code too for my work

@janhardo thank you so much 

@Rouben Rostamian  i have two question! one is personal :  regarding to your name are you persian?
secondly: how you give the initial condition to system is arbitrary?

@Rouben Rostamian  thank you so much, i will ask more question about this topic