caa a22 4500 606166203 CHVBK 20210128100657.0 cr unu---uuuuu 210128e20151201xx s 000 0 eng 10.1007/s10440-014-9983-z doi (NATIONALLICENCE)springer-10.1007/s10440-014-9983-z Dynamics of a Diffusive Predator-Prey Model with Modified Leslie-Gower Term and Michaelis-Menten Type Prey Harvesting [Elektronische Daten] [Yan Li, Mingxin Wang] A diffusive predator-prey model with modified Leslie-Gower term and Michaelis-Menten type prey harvesting subject to the homogeneous Neumann boundary condition is considered. We obtain the local and global stability of constant equilibria by eigenvalue analysis and iteration technique. Choosing some parameter concerning with harvesting as Hopf bifurcation parameter, we conclude the existence of periodic solutions near positive constant equilibrium. Using the normal form and center manifold theory, and numerical simulations, we demonstrate our theoretical results of stability and direction of periodic solutions. We also derive the non-existence and existence of non-constant positive steady states by energy method and degree theory. Springer Science+Business Media Dordrecht, 2014 Michaelis-Menten type prey harvesting nationallicence Global stability nationallicence Hopf bifurcation nationallicence Stationary pattern nationallicence Degree theory nationallicence Normal form nationallicence Center manifold nationallicence Li Yan Department of Mathematics, Harbin Institute of Technology, 150080, Harbin, PR China aut Wang Mingxin Natural Science Research Center, Harbin Institute of Technology, 150080, Harbin, PR China aut Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 147-172 0167-8019 140:1<147 2015 140 10440 https://doi.org/10.1007/s10440-014-9983-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10440-014-9983-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Li Yan Department of Mathematics, Harbin Institute of Technology, 150080, Harbin, PR China aut NATIONALLICENCE 700 1- Wang Mingxin Natural Science Research Center, Harbin Institute of Technology, 150080, Harbin, PR China aut NATIONALLICENCE 773 0- Acta Applicandae Mathematicae Springer Netherlands 140/1(2015-12-01), 147-172 0167-8019 140:1<147 2015 140 10440