This paper is concerned with the asymptotic stability of wave fronts and oscillatory waves for some predator-prey models. By spectral analysis and applying Evans function method with some numerical simulations, we show that the two types of waves with noncritical speeds are spectrally stable and nonlinearly exponentially stable in some exponentially weighted spaces.

中文翻译：

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某些捕食者-食饵模型的两种行波的渐近稳定性。

本文关注的是某些捕食-被捕食模型的波前和振荡波的渐近稳定性。通过频谱分析并在一些数值模拟中应用Evans函数方法，我们发现在某些指数加权空间中，两种非临界速度的波在频谱上是稳定的，并且在非线性指数上是稳定的。