Analysis of positive steady-state solutions for a class of Leslie-Gower predator-prey model with Holling-Ⅲ functional response
Purposes—To investigate the existence and stability of positive steady-state solutions for a Leslie-Gower predator-prey model with Holling Ⅲ functional response,and verify the obtained theoretical results by numerical simulations.Methods—The qualitative analysis of positive steady-state solutions is carried out by using the theory of reaction-diffusion equation,and so is the quantita-tive analysis by using the numerical simulations technique.Results—The conditions for the existence and stability of positive steady-state solutions are established,with the effects of the species growth rate on positive steady-state solutions given.Conclusions—An appropriate high growth rate can make predator and prey coexist.At the same time,numerical simulations show that when prey growth rate is high,the numbers of predator are not strictly increasing with respect to their growth rate.