Abstract
Abstract In this paper, asymptiotic stability of a nonlinear system in critical cases (NSICC) is studied. Two asymptotic stability criterions for NSICC with either a pair of pure imaginary eigenvalues or a simple zero eigenvalue are obtained by means of Lyapunov stability analysis and center manifold reduction technology . The two criterions proposed here mainly have two advantages: (l)the computation concerns only the second order derivatives instead of tedious manipulation of matrix; (2)the representation of the criterions reveals the relationship between the asymptotic stability of a NSICC and the modes of its linearized system.
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