Exact(17)
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).
Investigating the existence or non-existence of the limit cycle with order no less than 1 for models with state-dependent feedback control is challenging, but this problem has been addressed for some special cases [1].
Further, if (krightarrowinfty), then it is easy to show that there exists an unique asymptotically stable order-1 limit cycle and then for model (2.2) a limit cycle with order no less than 3 does not exist.
For case (SC11), we can employ the same methods as those for case (SC2) to prove that for model (2.2) a limit cycle with order no less than 3 does not exist.
Similar(43)
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