?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%2F4478%2F&rft.title=Persistent+Unstable+Equilibria+in+Wonderland&rft.creator=Gragnani%2C+A.&rft.creator=Milik%2C+A.&rft.creator=Prskawetz%2C+A.&rft.creator=Sanderson%2C+W.C.&rft.description=Models+of+the+interactions+between+population%2C+economy%2C+and+environment+often+contain+nonlinear+functional+relationships+and+variables+that+vary+at+different+speeds.+These+properties+foster+apparent+unpredictabilities+in+system+behavior.+Using+a+simple+deterministic+model+of+demographic%2C+economic+and+environmental+interactions%2C+we+illustrate+the+usefulness+of+geometric+singular+perturbation+theory+and+local+bifurcation+theory.+In+particular+we+show+how+it+is+possible+to+obtain+analytic+expressions+for%3A+(1)+the+level+of+emissions+above+which+environmental+deterioration+begins%2C+(2)+the+time+it+takes+from+reaching+the+critical+level+of+emissions+to+the+beginning+of+rapid+environmental+deterioration%2C+and+(3)+the+level+of+emissions+at+the+time+that+rapid+deterioration+begins.+Because+our+results+are+analytic%2C+they+make+the+outcomes+of+demographic%2C+economic%2C+and+environmental+interactions+more+predictable%2C+and%2C+therefore%2C+potentially+more+manageable.&rft.publisher=WP-95-118&rft.date=1995-11&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4478%2F1%2FWP-95-118.pdf&rft.identifier=++Gragnani%2C+A.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1294.html%3E%2C+Milik%2C+A.%2C+Prskawetz%2C+A.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F100.html%3E%2C+%26+Sanderson%2C+W.C.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F265.html%3E++(1995).++Persistent+Unstable+Equilibria+in+Wonderland.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-95-118+++++