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For model (2.2) a limit cycle with order no less than 3 does not exist.
These studies also found that the models have no limit cycles with order no less than 3.
In the following we prove that if (taugeqtau_{M}), then for model (2.2) no limit cycle with order no less than 3 exists for case (SC2).
In conclusion, we have proved that model (2.2) does not have a limit cycle with order no less than 3 for all cases, and consequently the result shown in Theorem 10.1 is true.
These results indicate that model (2.2) does not have any limit cycle with order no less than 2. Figure 15 Existence of periodic solution for case (SC (pmb{_{12}}) ).
Further, according to Lemma 10.3 and Remark 10.1 it is easy to see that if (tau=0) then for model (2.2) a limit cycle with order no less than 2 does not exist.
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