A generalized stochastic Nicholson blowfly model with mixed time-varying lags and harvest control: almost periodic oscillation and global stable behavior

The Nicholson blowfly model is an important differential equation and has been studied extensively and deeply. Real-world population dynamics models are often subject to many uncertainties. In random perspective, we delve into a generalized Nicholson blowfly model with mixed time-varying lags and control. We first establish an important exponential integral inequality with delay. Based on this inequality, we next use the nonlinear alternative of Leray-Schauder and Bochner’s double sequence criterion to study the existence and uniqueness of almost periodic solutions in distribution sense. Meanwhile, we further derive that the model remains almost periodic globally exponentially stable in mean square sense. Finally, some examples and simulations are designed to examine that our findings are correct and effective.