I'm trying to model a basic feedback system with delayed feedback. I've done the initial setup and now want to add a few more advanced features to my system.
Currently, it's just a simple delayed-differential equation with manipulatable delay to show how increasing the delay can send the system out of equilibrium.
What I'd like to add, however, is the ability for the system to be perturbed at a particular point in time. For example, in the Predator-Prey model this might mean that the system acts exactly as normal at all times against the given initial condition, but suddenly at t = T, where T is the perturbation point, either the number of predators or prey is shocked.
I want to model how this affects equilibrium for various parameters. Any good places to start?
Thanks again!
Edit:
What I have initially is -
Manipulate[ HumanFaucetSystem = NDSolve[{y'[time] + a*y[time - delay] == 0, y[time /; time <= 0] == deviation}, y, {time, 0, 200*delay + 1}]; Plot[Evaluate[y[x] /. HumanFaucetSystem], {x, 0, 100*delay + 1}, PlotRange -> All], {{delay, 0, "Delay"}, 0, 15}, {{a, 1, "Multiplier"}, -5, 5}, {{deviation, 25, "Initial Deviation"}, 0, 100}] I want to add another interactive parameter to the system that allows the user to schedule a specific time point at which a certain perturbation will occur. This can be positive or negative in the value of y.
On this logic, I want to expand it to a two-agent delayed system that I've modeled already but add this feature.