How to plot a Bifurcation diagram for differential equation? Is there any formula to plot the bifurcation diagram?

How to plot a Bifurcation diagram for differential equation? Is there any formula to plot the bifurcation diagram?

[Lazaros Moysis]

The best way to plot the bifurcation diagram is to use the local maxima method. Basically, you run a for loop, where each time you change the values of the system's parameter that you want to study. They you simulate the system, find the local maxima for a chosen state, and plot then in a graph. Once the for loop finishes, you can observe how many local maxima the system has for each parameter value. 1 local maxima means period-1 behavior, 2 local maxima means period-2 behavior and so on. Innumerable number of maxima means chaos

https://www.youtube.com/watch?v=jkrmZB9OM2E

https://www.youtube.com/watch?v=p9mg6TOBMY0

Answer 1

[KSSV]

http://www.math.le.ac.uk/people/rld8/ma1251/lab3.html

http://stackoverflow.com/questions/10693525/generate-bifurcation-diagram-for-2d-system

[DEEPIHA PADMANATHAN]

Thank you for the response Sir.

Answer 2

[Jagdeep Singh]

r1=10; r2=5; r3=3; a = 0.4; b = 1.5; c = 10; d = 1; e = 5; f = 1; g = 0.1; h=1.5; l=1; k=0.3; H=0.5;

dN = [n(1)*(r1-a*n(1)-b*n(2)-(c*n(3))/(1+g*n(1))-H); n(2)*(-r2+d*n(1)-e*n(2)-(f*n(3))/(1+g*n(2))-H); n(3)*(-r3+(h*n(1))/(1+g*n(1))+(l*n(1))/(1+g*n(2))-k*n(3)-H)];

How can I plot a Bifurcation diagram for avobe differential equation? may be N1 vs r1 or r2 or r3 or N2 vs r2

Thank you so much.