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), xt₀ = x₀ y(σ(t)) = g(t, y_t), yt₀ = y₀ 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.