#### Bo Sang, Qin-Long Wang, Brigita Fercec, Four limit cycles in a generalized Moon-Rand system with fifth-order perturbation, 2016 (2016), Article ID 14 (2 April 2016)

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Abstract

Based on our previous work for 2-dimensional systems, this paper introduces a method for computing focal values of a class of 3-dimensional systems, for which the Maple procedures are presented in the Appendix.  Using the ${\epsilon}^{1}$–order focal values computation, it is shown that a generalized Moon-Rand system with fifth-order perturbation can have 4 small-amplitude limit cycles around an equilibrium. The methodology developed in this paper can be used to consider bifurcation of limit cycles in higher-dimensional systems.