I get two different trajectoriesf or identical parametres, time, and initial condition.

for comparison i using integrator from Julia and python. I have used several integrators from Julia and python and get completely different results. Even when I imported an integrator with scipy to Julia, the result did not change.

Code from python

```
Gamma = lambda x_i: 1 / (1 + np.exp(-lambd * (x_i - Theta)))
def two_HRs(t, X, k1, k2):
x1, y1, z1, x2, y2, z2 = X
dx1 = y1 - a*x1**3 + b*x1**2 -z1 + I - k1*(x1 - v_s) * Gamma(x2)
dy1 = c - d*x1**2 - y1
dz1 = r*(s*(x1 - x_r) - z1)
dx2 = y2 - a*x2**3 + b*x2**2 -z2 + I - k2*(x2 - v_s) * Gamma(x1)
dy2 = c - d*x2**2 - y2
dz2 = r*(s*(x2 - x_r) - z2)
return [dx1, dy1, dz1, dx2, dy2, dz2]
a = 1
b = 3
c = 1
d = 5
x_r = -1.6
r = 0.01
s = 5
I = 4
v_s = 2
lambd = 10
Theta = -0.25
k1 = -0.17
k2 = -0.17
initials = [0.1, 0.1, 0.1, 0.1, 0.1, 0.1]
sol = solve_ivp(two_HRs, [0, 100000], initials, rtol = 1e-11, atol = 1e-11, args = (-0.17, -0.17), method="LSODA")
ts = sol.t
x1s, y1s, z1s, x2s, y2s, z2s = sol.y
```

i try use RK45, LSODA.

Code from Julia:

```
function sigma(x)
return 1.0 / ( 1.0 + exp( -10.0 * ( x - ( - 0.25 ) ) ) )
end
function HR(u, p, t)
a, b, c, d, s, xr, r, I, vs, k1, k2, el_link = p
x1, y1, z1, x2, y2, z2 = u
du1 = y1 + b * x1 ^ 2 - a * x1 ^3 - z1 + I - k1 * ( x1 - vs ) * sigma(x2) + el_link * ( x2 - x1 )
du2 = c - d * x1 ^2 - y1
du3 = r * ( s * ( x1 - xr ) - z1 )
du4 = y2 + b * x2 ^ 2 - a * x2 ^3 - z2 + I - k2 * ( x2 - vs ) * sigma(x1) + el_link * ( x1 - x2 )
du5 = c - d * x2 ^2 - y2
du6 = r * ( s * ( x2 - xr ) - z2 )
return SVector(du1, du2, du3,
du4, du5, du6)
end
a = 1.0; b = 3.0; c = 1.0; d = 5.0
xr = -1.6; r = 0.01; s = 5.0; I = 4.0; xv = 2.0
k12 = -0.17
k1= k12; k2 = k12
k = 0.0
condition = SA [0.1, 0.1, 0.1, 0.1, 0.1, 0.1]
tspan = (0.0, 100000.0)
p = SA[a, b, c, d, s, xr, r, I, xv, k1, k2, k];
probsa = ODEProblem(HR, condition, tspan, p)
sol = solve(probsa, AutoVern9(Rodas5()), abstol = 1e-11, reltol = 1e-11, dense=false, maxiters = 50000000);
```

Result from python

and Julia

in time series i using sum x1 + x2.

Also i try use

`dense = false`

and `dense = true`