Dissipativity of dynamical systems on time scales and the relationship between dissipative differential and dynamical systems

Abstract

This work is devoted to study the dissipativity property of dynamical systems on time scales and relationship between the dissipativity of systems of dynamic equations on time scales and the corresponding systems of ordinary differential equations. It is established that the dissipativity property is preserved when transitioning from equations on time scales $\mathbb{T}_\lambda$ to the corresponding ordinary differential equations and vice versa, provided that the graininess function $\mu_\lambda$ converges to zero as $\lambda\to0$.