Permanence of a Semi-Ratio-Dependent Predator-Prey System with Nonmonotonic Functional Response and Time Delay - Xuepeng Li; Wensheng Yang (Abstract and Applied Analysis)
Sufficient conditions for permanence of a semi-ratio-dependent predator-prey system with nonmonotonic functional response and time delay ̇𝑥1(𝑡)=𝑥1(𝑡)[𝑟1(𝑡)−𝑎11(𝑡)𝑥1(𝑡−𝜏(𝑡))−𝑎12(𝑡)𝑥2(𝑡)/(𝑚2+𝑥21(𝑡))],  ̇𝑥2(𝑡)=𝑥2(𝑡)[𝑟2(𝑡)−𝑎21(𝑡)𝑥2(𝑡)/𝑥1(𝑡)], are obtained, where 𝑥1(𝑡) and 𝑥2(𝑡) stand for the density of the prey and the predator, respectively, and 𝑚≠0 is a constant. 𝜏(𝑡)≥0 stands for the time delays due to negative feedback of the prey population.