No person shall trap or attempt to trap any animal on City public property except authorized personnel in the performance of their duties. Further, no person shall trap or allow the trapping of animals within the City corporate limits except on property zoned agricultural, and notice of intent to trap any of said areas must be annually filed in writing in advance with the Clerk by the owner and/or the trapper with the traps and trapping being in strict compliance with the appropriate statutes of the State and Rules and Regulations of the State Department of Natural Resources. Excepted from the provisions of this section are instant kill traps for the purpose of small rodent pest control on private property.