Existence and Global Attractivity of Positive Periodic Solutions in Shifts δ_± for a Nonlinear Dynamic Equation with Feedback Control on Time Scales

摘要

This paper is concerned with a nonlinear dynamic equation with feedback control on time scales. Based on the theory of calculus on time scales, by using a fixed point theorem of strict-set-contraction, some criteria are established for the existence of positive periodic solutions in shifts δ_± of the system; then, by using some differential inequalities and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the global attractivity of the system are obtained. Finally, two numerical examples are presented to illustrate the feasibility and effectiveness of the results.