Stability and Periodicity of Solutions for Delay Dynamic Systems on Time Scales

This article concerns the stability and periodicity of solutions to the delay dynamic system x4(t) = A(t)x(t) + F (t, x(t), x(g(t))) + C(t) on a time scale. By the inequality technique for vectors, we obtain some stability criteria for the above system. Then, using the Horn fixed point theorem, we present some conditions under which our system is asymptotically periodic and its periodic solution is unique. In particular, the periodic solution is positive under proper assumptions.