We study the exponential stability of a trivial invariant manifold of nonlinear extension of the dynamical system on a torus with impulsive jumps at nonfixed moments of time. The deduced sufficient conditions for the exponential stability of the trivial torus take into account the information on the qualitative properties of the dynamics of the system on the invariant manifold and weaken sufficient conditions available in the literature for a wide class of dynamical systems. New theorems impose constraints on a nonwandering set of the dynamical system guaranteeing the exponential stability of trivial manifold and are especially beneficial for the stability analysis of the extensions of dynamical systems with simple structures of the limit sets and recurrent trajectories.
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Published in Neliniini Kolyvannya, Vol. 22, No. 2, pp. 280–288, April–June, 2019.
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Feketa, P., Meurer, T., Perestyuk, M.M. et al. Exponential Stability of Invariant Manifold for a Nonlinear Impulsive Multifrequency System. J Math Sci 249, 694–703 (2020). https://doi.org/10.1007/s10958-020-04966-z