Below are a number of common chaotic systems and their parameters (some representing new previously unpublished calculations), collected here for convenience.  The least significant digit is only a best estimate.  A good project would be to improve the precision of the values and to add other cases.

Logistic map

• X_n+1 = AX_n(1 - X_n)
• Usual parameter: A = 4
• Lyapunov exponent (base-e): l = ln(2) = 0.693147181...
• Kaplan-Yorke dimension: D_KY = 1.0 (exact value)
  
• Correlation dimension: D₂ = 1.0 (exact value, converges slowly)
• Ref: R. May, Nature 261, 45-67 (1976)

Hénon map

• X_n+1 = 1 + Y_n - aX_n²
• Y_n+1 = bX_n
• Usual parameters: a = 1.4, b = 0.3
• Lyapunov exponents (base-e): l = 0.41922, -1.62319
• Kaplan-Yorke dimension: D_KY = 1.25827
• Correlation dimension: D₂ = 1.220 + 0.036
  
• Ref: M. Hénon, Commun. Math. Phys. Phys. 50, 69-77 (1976)

Chirikov (standard) map

• X_n+1 = X_n + Y_n+1 mod 2pi
• Y_n+1 = Y_n + k sin X_n mod 2pi
• Usual parameter: k = 1
• Lyapunov exponents (base-e): l = 0.10497, -0.10497
• Kaplan-Yorke dimension: D_KY = 2.0 (exact value)
  
• Correlation dimension: D₂ = 1.954 + 0.077
• Ref: B. V. Chirikov, Physics Reports 52, 263-379 (1979)

Lorenz attractor

• dx/dt = s(y - x)
• dy/dt = -xz + rx - y
• dz/dt = xy - bz
• Usual parameters: s = 10, r = 28, b = 8/3
• Lyapunov exponents (base-e): l = 0.9056, 0, -14.5723
• Kaplan-Yorke dimension: D_KY = 2.06215
• Correlation dimension: D₂ = 2.068 + 0.086
  
• Ref: E. N. Lorenz, J. Atmos. Sci. 20, 130-141 (1963)

Rössler attractor

• dx/dt = -y - z
• dy/dt = x + ay
• dz/dt = b + z(x - c)
• Usual parameters: a = b = 0.2, c = 5.7
• Lyapunov exponents (base-e): l = 0.0714, 0, -5.3943
• Kaplan-Yorke dimension: D_KY = 2.0132
• Correlation dimension: D₂ = 1.991 + 0.065 (converges slowly)
• Ref: O. E. Rössler, Phys. Lett. 57A, 397-398 (1976)

Ueda attractor

dx/dt = y

dy/dt = -x³ - ky + B sin z

dz/dt = 1

Usual parameters: B = 7.5, k = 0.05

Lyapunov exponents (base-e): l = 0.1034, 0, -0.1534

Kaplan-Yorke dimension: D_KY = 2.6741

Correlation dimension: D₂ = 2.675 + 0.132

Ref: Y. Ueda, J. Stat. Phys. 20, 181-196 (1979)

Simplest quadratic dissipative chaotic flow

dx/dt = y

dy/dt = z

dz/dt = -Az + y² - x

Usual parameter: A = 2.017

Lyapunov exponents (base-e): l = 0.0551, 0, -2.0721

Kaplan-Yorke dimension: D_KY = 2.0266

Correlation dimension: D₂ = 2.187 + 0.075 (converges slowly)

Ref: J. C. Sprott, Phys. Lett. A 228, 271-274 (1977)

Simplest piecewise linear dissipative chaotic flow

dx/dt = y

dy/dt = z

dz/dt = -Az - y - |x| + 1

Usual parameter: A = 0.6

Lyapunov exponents (base-e): l = 0.0362, 0, -0.6362

Kaplan-Yorke dimension: D_KY = 2.0569

Correlation dimension: D₂ = 2.131 + 0.072 (converges slowly)

Ref: S. J. Linz and J. C. Sprott, Phys. Lett. A 259, 240-245 (1999)

A more extensive list of such systems is included in the paper Improved Correlation Dimension Calculation, and an even more extensive list (62 cases) is in Appendix A of the book Chaos and Time-Series Analysis by J. C. Sprott (Oxford University Press, 2003).

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