Delay Differential Equations of Ecological Systems with Allee Effect

As it has been seen in previous chapters, delay differential equations exhibit much more complicated dynamics than ordinary differential equations since a time-delay could cause a stable equilibrium to become unstable and cause the populations to fluctuate. In this chapter, we study delay differential equations of prey-predator systems with the Allee effect. The dynamic relationship between the prey and their predators has long been and will continue to be one of the dominant themes in ecology due to its universal existence and importance (see, e.g., [1–4]).