Geometric properties of solution of a cylindrical dynamic system with impulsive state feedback control

A kind of cylindrical dynamic system with impulsive state feedback control is formulated and investigated. Based on the qualitative properties of the corresponding continuous system, the existence of order-k(k∈Z+) periodic solutions of the cylindrical dynamic system with impulsive state feedback control is discussed on the cylinder with perimeter 2π2π. If the equilibrium of the corresponding continuous system in the rectangle coordinate system is an unstable node, then the cylindrical dynamic system has two one-side stable minimum limit sets. If the equilibrium is an unstable focus, then, for different parameters, the cylindrical dynamic system has the periodic solutions with different periods and different orders. Finally, numerical simulations are given to verify the theoretical results.