Rate of Decay of Stable Periodic Solutions of Duffing Equations

Details Rate of Decay of Stable Periodic Solutions of Duffing Equations Rate of Decay of Stable Periodic Solutions of Duffing Equations

2007-03-27

arxiv.org/abs/math/0703816v1

Mathematics

Classical Analysis and ODEs

Key words: Periodic solution; Stability; Rate of decay

Scientific paper

In this paper, we consider the second-order equations of Duffing type. Bounds
for the derivative of the restoring force are given that ensure the existence
and uniqueness of a periodic solution. Furthermore, the stability of the unique
periodic solution is analyzed; the sharp rate of exponential decay is
determined for a solution that is near to the unique periodic solution.

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