dx/dt = -y - z

dy/dt = x + A y

dz/dt = B + z (x - C)

parameters: A = B = 0.2, C = 5.7
The step size of the fourth-order Runge-Kutta method: 0.0001

Lyapunov exponents (log with base-e): 0.066164, 0.003035, -5.399760

Lyapunov dimension: 2.012815

#----------------------------------------------

sum of the Lyapunov exponents: -5.3305614102

average trace of the Jacobian matrix: -5.3305614102

#----------------------------------------------

The trace of the Jacobian matrix of the Rössler system is A + x - C.  Therefore, the sum of the Lyapunov exponents is theoretically equal to A + <x> - C, where <x> is the time average of x.

Reference

An equation for continuous chaos

Otto Eberhard Rössler

Physics Letters A 57, 397-398 (1976)

DOI: 10.1016/0375-9601(76)90101-8