Periodic solutions of Simple Chaotic system in 3D via the second order Averaging method

Adnan A. Jalal, Niazy H. Hussein, Azad I. Amen, Nejmaddin A. Sulaiman

Sprott [2015] introduced a chaotic system ET9 with only one non-hyperbolic equilibrium point. This equilibrium is nonlinearity unstable and strange attractor is self-excited. Adding three parameters to the Sprott ET9 system, we obtain the autonomous system , where are real parameters. In this paper, we apply the averaging theory of second order to show the existence of limit cycles bifurcating from a degenerate zero-Hopf equilibrium at the origin. From one family we can prove that exactly 2 unstable limit cycles bifurcate simultaneously.

Volume 12 | 02-Special Issue

Pages: 240-246

DOI: 10.5373/JARDCS/V12SP2/SP20201066