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.

中文翻译：

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行为不均匀会破坏结构稳定性吗？

如果非均匀行为会破坏非线性系统的结构稳定性，则本文提供了一个答案。我们表明，如果线性系统$ \ dot {x}（t）= A（t）x（t）$接受非均匀指数二分法，那么被摄动的非自治系统$ \ dot {x}（t）= A（t x（t）+ f（t，x）$在合适的条件下结构稳定。