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We investigate the nonmonotonic behavior observed in the time-like nucleonelectromagnetic form factors. Using a phenomenological extending vector mesondominance model, where the ground states $\rho$ and $\omega$ and their excitedstates $\rho(2D)$, $\omega(3D)$, and $\omega(5S)$ are taken into account, wehave successfully reproduced the cross sections of $e^+ e^- \to p \bar{p}$ and$e^+ e^- \to n \bar{n}$ reactions. Furthermore, we have derived the nucleonelectromagnetic form factors in the time-like region, and it is found that theso-called periodic behaviour of the nucleon effective form factors is notconfirmed. However, there are indeed nonmonotonic structures in the line shapeof nucleon effective form factors, which can be naturally reproduced byconsidering the contributions from the low-lying excited vector states.

Understanding oscillating features of the time-like nucleon electromagnetic form factors within the extending vector meson dominance model