  Estimation of the degree of stability and the bounds of solutions to
non-autonomous nonlinear systems present major concerns in numerous applied
problems. Yet, current techniques are frequently yield overconservative
conditions which are unable to effectively gage these characteristics in
time-varying nonlinear systems. This paper develops a novel methodology
providing successive approximations to solutions that are stemmed from the
trapping and stability regions of these systems and estimate the errors of such
approximations. In turn, this leads to successive approximations of both the
bilateral bounds of solutions and the boundaries of trapping and stability
regions of the underlying systems. Along these lines we formulate enhanced
stability and boundedness criteria and contrast our inferences with inclusive
simulations.
