In this paper, we try to study the existence and uniqueness of affine-periodic solutions for the perturbed affine-periodic system. We prove that, under certain conditions, if the coefficient of the forced term is sufficiently small, then the system admits affine-periodic solutions which have the form of z(t+T,μ)=Qz(t,μ) with some nonsingular matrix Q. Depending on the structure of Q, they may be periodic, anti-periodic, quasi-periodic or even unbounded spiral motions. The main tools we used are the theory of exponential dichotomy and Banach contraction mapping principle.
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Dong et al. (2022) studied this question.
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