Sprott  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