?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%2F4953%2F&rft.title=Complex+Dynamics+in+Romantic+Relationships&rft.creator=Gragnani%2C+A.&rft.creator=Rinaldi%2C+S.&rft.creator=Feichtinger%2C+G.&rft.description=Minimal+models+composed+of+two+ordinary+differential+equations+are+considered+in+this+paper+to+mimic+the+dynamics+of+the+feelings+between+two+persons.+In+accordance+with+attachment+theory%2C+individuals+are+divided+into+secure+and+non-secure+individuals%2C+and+in+synergic+and+non-synergic+individuals%2C+for+a+total+of+four+different+classes.+Then%2C+it+is+shown+that+couples+composed+of+secure+individuals%2C+as+well+as+couples+composed+of+nonsynergic+individuals+can+only+have+stationary+modes+of+behavior.+By+contrast%2C+couples+composed+of+a+secure+and+synergic+individual+and+a+non-secure+and+non-synergic+individual+can+experience+cyclic+dynamics.+In+other+words%2C+the+coexistence+of+insecurity+and+synergism+in+the+couple+is+the+minimum+ingredient+for+complex+love+dynamics.+The+result+is+obtained+through+a+detailed+local+and+global+bifurcation+analysis+of+the+model.+Supercitical+Hopf%2C+fold+and+homoclinic+bifurcation+curves+are+numerically+detected+around+a+Bogdanov-Takens+codimension-2+bifurcation+point.+The+existence+of+a+codimension-2+homoclinic+bifurcation+is+also+ascertained.+The+bifurcation+structure+allows+one+to+identify+the+role+played+by+individual+synergism+and+reactiveness+to+partner's+love+and+appeal.+It+also+explains+why+aging+has+a+stabilizing+effect+on+the+dynamics+of+the+feelings.+All+results+are+in+agreement+with+common+wisdom+on+the+argument.+Possible+extensions+are+briefly+discussed+at+the+end+of+the+paper.&rft.publisher=WP-96-074&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%2F4953%2F1%2FWP-96-074.pdf&rft.identifier=++Gragnani%2C+A.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1294.html%3E%2C+Rinaldi%2C+S.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F253.html%3E%2C+%26+Feichtinger%2C+G.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F2589.html%3E++(1996).++Complex+Dynamics+in+Romantic+Relationships.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-96-074+++++