{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2022,4,1]],"date-time":"2022-04-01T06:16:47Z","timestamp":1648793807165},"reference-count":30,"publisher":"World Scientific Pub Co Pte Lt","issue":"02","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Int. J. Bifurcation Chaos"],"published-print":{"date-parts":[[2007,2]]},"abstract":"<jats:p> In this paper, we propose a model for the dynamics of a fatal infectious disease in a wild animal population with birth pulses and pulse culling, where periodic birth pulses and pulse culling occur at different fixed times. Using the discrete dynamical system determined by stroboscopic map, we obtain an exact cycle of the system, and obtain the threshold conditions for its stability. Bifurcation diagrams are constructed with the birth rate (or culling effort) as the bifurcation parameter, and these are observed to display complex dynamic behaviors, including chaotic bands with period windows, period-doubling and period-halving bifurcations, pitch-fork and tangent bifurcations, nonunique dynamics (meaning that several attractors or attractor and chaos coexist), basins of attraction and attractor crisis. This suggests that birth pulses and pulse culling provide a natural period or cyclicity that makes the dynamical behaviors more complex. Moreover, we investigate the sufficient conditions for global stability of semi-trivial periodic solutions. <\/jats:p>","DOI":"10.1142\/s0218127407017392","type":"journal-article","created":{"date-parts":[[2007,5,14]],"date-time":"2007-05-14T07:22:06Z","timestamp":1179127326000},"page":"521-533","source":"Crossref","is-referenced-by-count":1,"title":["DYNAMIC COMPLEXITIES IN AN EPIDEMIC MODEL WITH BIRTH PULSES AND PULSE CULLING"],"prefix":"10.1142","volume":"17","author":[{"given":"SHUJING","family":"GAO","sequence":"first","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urungi 830046, P. R. China"},{"name":"College of Mathematics and Computer Science, Gannan Normal University, Ganzhou 341000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"LANSUN","family":"CHEN","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, P. R. China,"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"ZHIDONG","family":"TENG","sequence":"additional","affiliation":[{"name":"College of Mathematics and Systems Science, Xinjiang University, Urumqi 830046, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"DEHUI","family":"XIE","sequence":"additional","affiliation":[{"name":"College of Business Administration, Gannan Normal University, Ganzhou 341000, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2011,11,20]]},"reference":[{"key":"rf1","volume-title":"The Population Dynamics of Infectious Diseases: Theory and Application","author":"Anderson R. 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