A new chaotic attractor coined. (English) Zbl 1063.34510

The authors deal with a new chaotic attractor generated by the following simple three-dimensional autonomous system \[ \dot x= a(y- x),\quad\dot y= -xz+ cy,\quad\dot z= xy- bz.\tag{1} \] Obviously, (1) is not diffeomorphic to the Lorenz and Chen system since the eigenvalue structures of their corresponding equilibrium points are not equivalent. It is straightforward but somewhat tedious to verify that there is no nonsingular coordinate transformation that can map one system into the other. Therefore, they are all not topologically equivalent.


34D45 Attractors of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI


[1] Celikovský S., Int. J. Bifurcation and Chaos
[2] DOI: 10.1142/3033 · doi:10.1142/3033
[3] DOI: 10.1142/S0218127499001024 · Zbl 0962.37013 · doi:10.1142/S0218127499001024
[4] DOI: 10.1007/978-1-4612-5767-7 · doi:10.1007/978-1-4612-5767-7
[5] Ueta T., Int. J. Bifurcation and Chaos 10 pp 1917–
[6] Vanecek A., Control Systems: From Linear Analysis to Synthesis of Chaos (1996)
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