#Proj5.txt: Maple package for Project 5 of Math 336 (Rutgers University, Fall 2025 taught by Dr. Z. (aka Professor Doron Zeilberger))




read `DMB.txt`:


#Intro text
print(`This is Proj5.txt, a Maple package accompanying Project X of Dr. Z.'s Math 336 (Dynamical Models in Biology), Fall 2025`):
print(`Project Leader: Alyssa Lee`):
print(``):
print(`Other members: Victoria Serafin, Shakthi Venkatesan`):
print(``):
print(`For a list of the procedures done by this team type: Help5(); For Help with a specific procedure, type: Help5(ProcedureName);`):


Help5:=proc()
if nargs=0 then
print(`The available procedures are: PlotGeneNet`):


elif nargs=1 and args[1]=”PlotGeneNet” then
print(`Usage: PlotGeneNet(a0,a,b,n,initial_conditions,step_size,end_time). a0,a,b,n are parameters of the M. Elowitz and S. Leibler repressilator model, described in the Ellner-Guckenheimer book, Eq. (4.1) (chapter 4,  p. 112). initial_conditions is a list of initial conditions for [m1, m2, m3, p1, p2, p3]. step_size in the range (0,0.1]. end_time is the time at which the simulation should end. Try PlotGeneNet(0, 50, 0.2, 2, [0.2, 0.1, 0.3, 0.1, 0.4, 0.5], 0.1, 100)`):


else
print(`There is no Help for`, args):
fi:


end:




#Example: PlotGeneNet(0, 50, 0.2, 2, [0.2, 0.1, 0.3, 0.1, 0.4, 0.5], 0.1, 100)
#Red=mlacI,


PlotGeneNet:=proc(a0,a,b,n,initial_conditions,step_size,end_time) local L,i1,i2,i3,i4,i5,i6:


if not (type(initial_conditions,list) and type(step_size,numeric) and step_size<=0.1 and type(end_time,numeric) and end_time>0) then
 print(`bad input`):
 RETURN(FAIL):
fi:


L:=Dis(GeneNet(a0,a,b,n,m1,m2,m3,p1,p2,p3), [m1, m2, m3, p1, p2, p3],initial_conditions,step_size,end_time):
plot([[seq([L[i1][1],L[i1][2][1]],i1=1..nops(L))],[seq([L[i2][1],L[i2][2][2]],i2=1..nops(L))],[seq([L[i3][1],L[i3][2][3]],i3=1..nops(L))],[seq([L[i4][1],L[i4][2][4]],i4=1..nops(L))],[seq([L[i5][1],L[i5][2][5]],i5=1..nops(L))],[seq([L[i6][1],L[i6][2][6]],i6=1..nops(L))]]):
end: