Existence and stability of stationary waves of a population model with strong Allee effect

We investigate the existence and stability of stationary waves of a nonlocal reaction-diffusion population model with delay, nonlocality and strong Allee effect. By reducing the model, the conditions for existence of stationary wavefront, wave pulse and inverted wave pulse are established. Then we show that the stationary waves of the reduced model are also the stationary waves of the general model. The global stability of the stationary waves is illustrated by numerically solving the general model for different sets of parameter values.

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