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Does nonuniform behavior destroy the structural stability?

  • Received: 13 May 2020 Accepted: 23 June 2020 Published: 01 July 2020
  • MSC : 37F15, 34D09, 37B55, 37D25

  • This paper provides an answer if the nonuniform behavior can destroy the structural stability of nonlinear systems. We show that if the linear system $\dot{x}(t) = A(t)x(t)$ admits a nonuniform exponential dichotomy, then the perturbed nonautonomous system $\dot{x}(t) = A(t)x(t)+f(t, x)$ is structurally stable under suitable conditions.

    Citation: Yuzhen Bai, Donal O’Regan, Yong-Hui Xia, Xiaoqing Yuan. Does nonuniform behavior destroy the structural stability?[J]. AIMS Mathematics, 2020, 5(6): 5628-5638. doi: 10.3934/math.2020359

    Related Papers:

  • This paper provides an answer if the nonuniform behavior can destroy the structural stability of nonlinear systems. We show that if the linear system $\dot{x}(t) = A(t)x(t)$ admits a nonuniform exponential dichotomy, then the perturbed nonautonomous system $\dot{x}(t) = A(t)x(t)+f(t, x)$ is structurally stable under suitable conditions.


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