?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4951%2F&rft.title=Singular+Homoclinic+Bifurcations+in+Tri-trophic+Food+Chains&rft.creator=Feo%2C+O.+de&rft.creator=Rinaldi%2C+S.&rft.description=The+Rosenzweig-MacArthur+food+chain+model+is+proved+to+have+homoclinic+orbits.+The+proof+is+in+two+steps.+First+we+use+a+geometric+approach+based+on+singular+perturbation+and+detect+singular+homoclinic+orbits+as+well+as+parameter+combinations+for+which+these+orbits+exist.+Then+we+show%2C+numerically%2C+that+for+slightly+different+parameter+values+there+exist+also+non+singular+homoclinic+orbits+which+tend+toward+the+singular+ones+when+the+time+responses+of+the+three+trophic+levels+are+extremely+diversified.+The+analysis+is+performed+systematically%2C+without+exploiting+too+deeply+the+mathematical+structure+of+the+Rosenzweig-MacArthur+model.+This+is+done+intentionally%2C+in+order+to+facilitate+readers+interested+more+in+the+methodology+than+in+the+application+to+food+chains.&rft.publisher=WP-96-076&rft.date=1996-07&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4951%2F1%2FWP-96-076.pdf&rft.identifier=++Feo%2C+O.+de+%26+Rinaldi%2C+S.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F253.html%3E++(1996).++Singular+Homoclinic+Bifurcations+in+Tri-trophic+Food+Chains.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-96-076+++++