Hopf bifurcation of a generalized Moon–Rand system

• The Moon–Rand systems were developed to model the control of flexible space structures, see [2], [6] and [8].
• In [6] it is shown that the quadratic Moon–Rand system can have 2 limit cycles in a Hopf bifurcation.
• Here we show that the cubic Moon-Rand system can have 18 limit cycles in a Hopf bifurcation.
• Our method can be applied to other differential systems.

We study the Hopf bifurcation from the equilibrium point at the origin of a generalized Moon–Rand system. We prove that the Hopf bifurcation can produce 8 limit cycles. The main tool for proving these results is the averaging theory of fourth order. The computations are not difficult, but very big and have been done with the help of Mathematica and Mapple.