TY - JOUR AU - Muhammadhaji, Ahmadjan PY - 2019 TI - Permanence and extinction in a periodic ratio-dependent population system with stage structure JO - Mathematics in Natural Science SP - 20--28 VL - 5 IS - 1 AB - This paper studies a class of nonautonomous two-species ratio-dependent population system with stage structure. Some sufficient conditions on the boundedness, permanence, extinction, and periodic solution of the system are established by using the comparison method. SN - ISSN 2600-7665 UR - http://dx.doi.org/10.22436/mns.05.01.03 DO - 10.22436/mns.05.01.03 ID - Muhammadhaji2019 ER - TY - BOOK TI - Models and Research Methods of Mathematical Ecology AU - L. Chen PB - Science Press PY - 1988 DA - 1988// CY - Beijing ID - Chen1988 ER - TY - JOUR TI - Permanence, extinction and periodic solution of the predator-prey system with Beddington-DeAngelis functional response and stage structure for prey AU - F. D. Chen AU - M. S. You JO - Nonlinear Anal. Real World Appl. PY - 2008 DA - 2008// VL - 9 ID - Chen2008 ER - TY - JOUR TI - The effect of dispersal on population growth with stage-structure AU - J. G. Cui AU - L. S. Chen AU - W. D. Wang JO - Comput. Math. Appl. PY - 2000 DA - 2000// VL - 39 ID - Cui2000 ER - TY - JOUR TI - Rich dynamics of a ratiodependent one prey two predators model AU - S. Hsu AU - T. Hwang AU - Y. Kuang JO - J. Math. Biol. PY - 2001 DA - 2001// VL - 43 ID - Hsu2001 ER - TY - JOUR TI - Permanence and periodicity of a delayed ratio-dependent predator-prey model with Holling type functional response and stage structure AU - Z. X. Li AU - L. S. Chen AU - J. M. Huang JO - J. Comput. Appl. Math. PY - 2009 DA - 2009// VL - 233 ID - Li2009 ER - TY - JOUR TI - Permanence of a predator-prey system with stage structure and time delay AU - Z.-H. Ma AU - Z.-Z. Li AU - S.-F. Wang AU - T. Li AU - F.-P. Zhang JO - Appl. Math. Comput. PY - 2008 DA - 2008// VL - 201 ID - Ma2008 ER - TY - BOOK TI - Theoretical Ecology, Principle and Applications AU - R. M. May PB - Sounders Press PY - 1976 DA - 1976// CY - Philadelphia ID - May1976 ER - TY - JOUR TI - Periodic solutions for n-species Lotka-Volterra competitive systems with pure delays AU - A. Muhammadhaji AU - R. Mahemuti AU - Z. D. Teng JO - Chin. J. Math. (N.Y.) PY - 2015 DA - 2015// VL - 2015 ID - Muhammadhaji2015 ER - TY - JOUR TI - Permanence and extinction analysis for a delayed ratio-dependent cooperative system with stage structure AU - A. Muhammadhaji AU - Z. D. Teng AU - X. Abdurahman JO - Afr. Mat. PY - 2014 DA - 2014// VL - 25 ID - Muhammadhaji2014 ER - TY - JOUR TI - The positive periodic slotion in periodic Kolmogorov type systems with delays AU - Z. Teng AU - L. Chen JO - Acta. Math. Appl. Sinica. PY - 1999 DA - 1999// VL - 22 ID - Teng1999 ER - TY - JOUR TI - A nonautonomous predator-prey system with stage structure and double time delays AU - J. Y. Wang AU - Q. S. Lu AU - Z. S. Feng JO - J. Comput. Appl. Math. PY - 2009 DA - 2009// VL - 230 ID - Wang2009 ER - TY - JOUR TI - Dynamics in a ratio-dependent predator-prey model with predator harvesting AU - D. M. Xiao AU - W. X. Li AU - M. Han JO - J. Math. Anal. Appl. PY - 2006 DA - 2006// VL - 324 ID - Xiao2006 ER - TY - JOUR TI - Permanence and periodicity of a delayed ratio-dependent predator-prey model with stage structure AU - R. Xu AU - M. A. J. Chaplain AU - F. A. Davidson JO - J. Math. Anal. Appl. PY - 2005 DA - 2005// VL - 303 ID - Xu2005 ER - TY - JOUR TI - The effect of stage-structure on the permanence of a predator-prey system with time delay AU - R. Xu AU - Z. Ma JO - Appl. Math. Comput. PY - 2007 DA - 2007// VL - 189 ID - Xu2007 ER - TY - JOUR TI - Periodic solutions of a nonautonomous predator-prey system with stage structure and time delays AU - R. Xu AU - Z. Q. Wang JO - J. Comput. Appl. Math. PY - 2006 DA - 2006// VL - 196 ID - Xu2006 ER - TY - JOUR TI - Periodic solutions of nonautonomous stage-structured cooperative system AU - Z. Q. Zhang AU - J. Wu AU - Z. C. Wang JO - Comput. Math. Appl. PY - 2004 DA - 2004// VL - 47 ID - Zhang2004 ER -