LF Olsen, H Degn - Quarterly reviews of biophysics, 1985

Reproduced and discussed in Strogatz Nonlinear Dynamics (2nd edition), Figure 10.6.7

```python import numpy as np import matplotlib.pyplot as plt from scipy.integrate import solve_ivp

def rossler_system(t, xyz, a, b, c):

   x, y, z = xyz
   dx_dt = -y - z
   dy_dt = x + a * y
   dz_dt = b + z * (x - c)
   return [dx_dt, dy_dt, dz_dt]

1. Rossler system parameters

a = 0.2 b = 0.2 c = 5

1. Initial conditions

xyz0 = [1.0, 1.0, 1.0] tmin, tmax = 0, 10000 t_span = [tmin, tmax] t_eval = np.linspace(t_span[0], t_span[1], (tmax-tmin) * t_resolution)

solution = solve_ivp(rossler_system, t_span, xyz0, args=(a, b, c), t_eval=t_eval) x, y, z = solution.y

def find_local_maxima(arr):

   local_maxima = []
   
   for i in range(1, len(arr) - 1):
       if arr[i - 1] < arr[i] > arr[i + 1]:
           local_maxima.append(arr[i])
   
   return local_maxima

local_maxima = find_local_maxima(x)

x = local_maxima[10:-1] y = local_maxima[11:]

z = np.polyfit(x, y, 5) p = np.poly1d(z) fig, ax = plt.subplots(figsize=(8, 6)) ax.scatter(local_maxima[10:-1], local_maxima[11:], s=0.01) ax.plot(sorted(x), p(sorted(x)), color='red', linewidth=0.2)

ax.set_xlabel("$x_{max}(n)$") ax.set_ylabel("$x_{max}(n+1)$") ax.set_title(f"Lorenz map for the Rössler attractor, with $a={a}, b={b}, c={c}$") plt.show()