Zero-Hopf Periodic Orbit of a Quadratic System of Differential Equations Obtained from a Third-Order Differential Equation

© 2017, Foundation for Scientific Research and Technological Innovation. We study the zero-Hopf bifurcation of the third-order differential equations x″′+(a1x+a0)x″+(b1x+b0)x′+x2=0,where a, a 1 , b and b 1 are real parameters. The prime denotes derivative with respect to an independent variable t. We also provide an estimate of the zero-Hopf periodic solution and their kind of stability. The Hopf bifurcations of these differential systems were studied in [5], here we complete these studies adding their zero-Hopf bifurcations.