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  A nonlinear autonomous stationary system with a locally unstable area



Data input for Infinity:

l1 := 0.1*diff(x1(t),t)-x1(t)-x2(t) = -x1(t)^3/3
l2 := -2*a*x1(t) + diff(x2(t),t) = -2*x1(t)^3
a := 1.2
SupT := 10
Complicated := 0
SupLocError := 1e-6
analysis({l1,l2, x1(0):=2, x2(0):=eval(2^3/3-a*2)},{x1(t),x2(t)},{0},{0}, {exp(log(2)-2*t), ((exp(log(2)-2*t))^3)/3-1.2*exp(log(2)-2*t)});


The answers received by Infinity if Complicated:=0.




The answers received by Infinity if Complicated:=1.


Digits := 100
l1:= 0.1*diff(x1(t),t)-x1(t)-x2(t) = -1/3*x1(t)^3;
l2:= -2*a*x1(t) + diff(x2(t),t) = -2*x1(t)^3;
a:=1.2;
SupT := 20
SupLocError := 1e-40
Complicated := 1

analysis({l1,l2, x1(0):=2, x2(0):=eval(2^3/3-a*2)},{x1(t),x2(t)},{0},{0}, {exp(log(2)-2*t), ((exp(log(2)-2*t))^3)/3-1.2*exp(log(2)-2*t)});





Data input for Maple:

x10 := 2: a := 1+2*mu: mu := 0.1:
ode1 := mu*diff(x1(t),t)-x1(t)-x2(t) = -x1(t)^3/3:
ode2 := -2*a*x1(t)+diff(x2(t),t) = -2*x1(t)^3:
sol := dsolve({ode1,ode2,x1(0) = x10, x2(0) = x10^3/3 - a*x10},{x1(t),x2(t)}, type =
numeric,method=taylorseries);
with(plots):
range0 := 0..10;
g1 := odeplot(sol,[t,x1(t)],range0,color= green, numpoints = 2000):
g2 := odeplot(sol,[t,x2(t)],range0,color = red, numpoints = 2000):
display(g1,g2);

Solutions received by Maple:
Neust.jpg (20480 Bytes)
Precise solutions:
plot([exp(log(2)-2*t), ((exp(log(2)-2*t))^3)/3-1.2*exp(log(2)-2*t)], t = 0..10);

NeustToch.jpg (12288 Bytes)
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