TOPICS
Search

Dadras System


The Dadras system is an autonomous quadratic dynamical system given by

x^'=y-ax+byz
(1)
y^'=cy+z-xz
(2)
z^'=dxy-hz,
(3)

where a, b, c, d, and h are positive parameters (Dadras and Momeni 2009). The state variables are x(t), y(t), and z(t), and primes denote derivatives with respect to time t. The origin is an equilibrium point. The Jacobian of the vector field there has eigenvalues -a, c, and -h, so the origin is a saddle point. The vector field has constant divergence c-a-h, so the flow contracts phase space volume if c<a+h. Dadras and Momeni (2009) report numerical examples of strange attractors with different numbers of scrolls, or spiral-shaped lobes in phase space, including a double-scroll attractor. Their two-wing example uses a=3, b=2.7, c=4.7, d=2, and h=9, with (x(0),y(0),z(0))=(5,0,-4).


See also

Dynamical System, Strange Attractor

Explore with Wolfram|Alpha

References

Dadras, S. and Momeni, H. R. "A Novel Three-Dimensional Autonomous Chaotic System Generating Two, Three and Four-Scroll Attractors." Phys. Lett. A 373, 3637-3642, 2009. https://doi.org/10.1016/j.physleta.2009.07.088.

Cite this as:

Weisstein, Eric W. "Dadras System." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DadrasSystem.html

Subject classifications