{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,7]],"date-time":"2026-05-07T00:14:23Z","timestamp":1778112863123,"version":"3.51.4"},"reference-count":16,"publisher":"World Scientific Pub Co Pte Lt","issue":"08","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2009,8]]},"abstract":"<jats:p> The objective of this paper is to study the dynamical properties of a Holling-type II predator\u2013prey system with constant rate harvesting. It is shown that the model has at most three equilibria in the first quadrant and can exhibit numerous kinds of bifurcation phenomena, including the saddle-node bifurcation, the degenerate Bogdanov\u2013Takens bifurcation of codimension 3, the supercritical and subcritical Hopf bifurcation, the generalized Hopf bifurcation. These results reveal far richer dynamics than that of the model with no harvesting. <\/jats:p>","DOI":"10.1142\/s021812740902427x","type":"journal-article","created":{"date-parts":[[2009,11,3]],"date-time":"2009-11-03T11:10:49Z","timestamp":1257246649000},"page":"2499-2514","source":"Crossref","is-referenced-by-count":39,"title":["BIFURCATIONS OF A HOLLING-TYPE II PREDATOR\u2013PREY SYSTEM WITH CONSTANT RATE HARVESTING"],"prefix":"10.1142","volume":"19","author":[{"given":"GUOJUN","family":"PENG","sequence":"first","affiliation":[{"name":"Department of Mathematics, Xi'an Jiao Tong University, Xi'an 710049, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"YAOLIN","family":"JIANG","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Xi'an Jiao Tong University, Xi'an 710049, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"CHANGPIN","family":"LI","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-0147-9"},{"key":"rf2","volume-title":"Mathematical Biophysics of Interacting Populations","author":"Bazykin A. D.","year":"1985"},{"key":"rf3","doi-asserted-by":"publisher","DOI":"10.1007\/BF00280586"},{"key":"rf4","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511665639"},{"key":"rf5","volume-title":"The Optimal Management of Renewable Resources","author":"Clark C. W.","year":"1990"},{"key":"rf6","doi-asserted-by":"publisher","DOI":"10.1137\/0143052"},{"key":"rf7","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127406014939"},{"key":"rf8","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1017\/S0143385700004119","volume":"7","author":"Dumortier F.","journal-title":"Erg. Th. Dyn. Syst."},{"key":"rf9","doi-asserted-by":"publisher","DOI":"10.1007\/BFb0098353"},{"key":"rf10","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4612-1140-2"},{"key":"rf11","first-page":"3","volume":"45","author":"Holling C. S.","journal-title":"Mem. Entomolog. Soc. Can."},{"key":"rf12","doi-asserted-by":"publisher","DOI":"10.1007\/s002850050105"},{"key":"rf13","doi-asserted-by":"publisher","DOI":"10.1142\/S0218127405014209"},{"key":"rf14","volume-title":"Elements of Applied Bifurcation Theory","author":"Kuznetsov Y. A.","year":"1998"},{"key":"rf15","volume-title":"Models in Ecology","author":"Smith J. M.","year":"1974"},{"key":"rf16","doi-asserted-by":"publisher","DOI":"10.2307\/1942114"}],"container-title":["International Journal of Bifurcation and Chaos"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S021812740902427X","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,7]],"date-time":"2019-08-07T14:55:49Z","timestamp":1565189749000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/abs\/10.1142\/S021812740902427X"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,8]]},"references-count":16,"journal-issue":{"issue":"08","published-online":{"date-parts":[[2011,11,20]]},"published-print":{"date-parts":[[2009,8]]}},"alternative-id":["10.1142\/S021812740902427X"],"URL":"https:\/\/doi.org\/10.1142\/s021812740902427x","relation":{},"ISSN":["0218-1274","1793-6551"],"issn-type":[{"value":"0218-1274","type":"print"},{"value":"1793-6551","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,8]]}}}