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A Hopf bifurcation criterion of fractional-order systems with order 1 <{\alpha} < 2 is established in this paper, in which all conditions areexplicitly expressed by parameters without solving the roots of the relevantcharacteristic polynomial of Hopf bifurcation conditions. It avoids the problemthat existing methods may fail due to the computational complexity in themulti-parameter situation. The bifurcation hyper-surface of multi-parameter canbe obtained directly.

An explicit Hopf bifurcation criterion of fractional-order systems with order 1 < {\alpha} < 2