%0 Journal Article %1 Huo2011 %A Huo, H.-F. %A Wang, X. %A Castillo-Chavez, C. %D 2011 %J Mathematical Problems in Engineering %K Boundedness Ecology Global Local Nonnegative Population Positive Predator-prey Sufficient attractivity; conditions, equilibria; equilibrium; models; of solution; stability; structures; %R http://dx.doi.org/10.1155/2011/149341 %T Dynamics of a stage-structured leslie-gower predator-prey model %U http://dx.doi.org/10.1155/2011/149341 %V 2011 %X A generalized version of the Leslie-Gower predator-prey model that incorporates the prey population structure is introduced. Our results show that the inclusion of (age) structure in the prey population does not alter the qualitative dynamics of the model; that is, we identify sufficient conditions for the trapping of the dynamics in a biological compact setalbeit the analysis is a bit more challenging. The focus is on the study of the boundedness of solutions and identification of sufficient conditions for permanence. Sufficient conditions for the local stability of the nonnegative equilibria of the model are also derived, and sufficient conditions for the global attractivity of positive equilibrium are obtained. Numerical simulations are used to illustrate our results. Â\copyright 2011 Hai-Feng Huo et al.

@article{Huo2011, abstract = {A generalized version of the Leslie-Gower predator-prey model that incorporates the prey population structure is introduced. Our results show that the inclusion of (age) structure in the prey population does not alter the qualitative dynamics of the model; that is, we identify sufficient conditions for the trapping of the dynamics in a biological compact setalbeit the analysis is a bit more challenging. The focus is on the study of the boundedness of solutions and identification of sufficient conditions for permanence. Sufficient conditions for the local stability of the nonnegative equilibria of the model are also derived, and sufficient conditions for the global attractivity of positive equilibrium are obtained. Numerical simulations are used to illustrate our results. {\^A}{\copyright} 2011 Hai-Feng Huo et al.}, added-at = {2017-11-10T22:48:29.000+0100}, affiliation = {Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China; Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, United States}, art_number = {149341}, author = {Huo, H.-F. and Wang, X. and Castillo-Chavez, C.}, biburl = {https://www.bibsonomy.org/bibtex/2a77b59670c02972992c0892d3483ba19/ccchavez}, correspondence_address1 = {Huo, H.-F.; Institute of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu 730050, China; email: hfhuo@lut.cn}, date-added = {2017-11-10 21:45:26 +0000}, date-modified = {2017-11-10 21:45:26 +0000}, document_type = {Article}, doi = {http://dx.doi.org/10.1155/2011/149341}, interhash = {73fe7f08e5bcf993b8979f8b150579dc}, intrahash = {a77b59670c02972992c0892d3483ba19}, issn = {1024123X}, journal = {Mathematical Problems in Engineering}, keywords = {Boundedness Ecology Global Local Nonnegative Population Positive Predator-prey Sufficient attractivity; conditions, equilibria; equilibrium; models; of solution; stability; structures;}, language = {English}, timestamp = {2017-11-10T22:48:29.000+0100}, title = {Dynamics of a stage-structured leslie-gower predator-prey model}, url = {http://dx.doi.org/10.1155/2011/149341}, volume = 2011, year = 2011 }