Criteria on boundedness in terms of two measures for dynamic systems

In this paper, we consider the following dynamic systems on time scales x(σ(t)) = f(t, x
_t
), xt
₀
= x
₀
y(σ(t)) = g(t, y
_t
), yt
₀
= y
₀
where σ(t) > t. By employing the concept of upper monotone increasing function and Lyapunov method, we obtain a new comparison theorem first, on this basis, some criteria on the boundedness in terms of two measures for these dynamic systems are obtained.