eprintid: 4953 rev_number: 25 eprint_status: archive userid: 351 dir: disk0/00/00/49/53 datestamp: 2016-01-15 02:07:51 lastmod: 2021-08-27 17:15:45 status_changed: 2016-01-15 02:07:51 type: monograph metadata_visibility: show item_issues_count: 2 creators_name: Gragnani, A. creators_name: Rinaldi, S. creators_name: Feichtinger, G. creators_id: 7287 creators_id: 7286 creators_id: 1555 title: Complex Dynamics in Romantic Relationships ispublished: pub internal_subjects: iis_met internal_subjects: iis_mod internal_subjects: iis_sys divisions: prog_dyn abstract: 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, individuals are divided into secure and non-secure individuals, and in synergic and non-synergic individuals, for a total of four different classes. Then, it is shown that couples composed of secure individuals, as well as couples composed of nonsynergic individuals can only have stationary modes of behavior. By contrast, couples composed of a secure and synergic individual and a non-secure and non-synergic individual can experience cyclic dynamics. In other words, 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, 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. date: 1996-07 date_type: published publisher: WP-96-074 iiasapubid: WP-96-074 price: 10 creators_browse_id: 1294 creators_browse_id: 253 creators_browse_id: 2589 full_text_status: public monograph_type: working_paper place_of_pub: IIASA, Laxenburg, Austria pages: 28 coversheets_dirty: FALSE fp7_type: info:eu-repo/semantics/book citation: Gragnani, A. , Rinaldi, S. , & Feichtinger, G. (1996). Complex Dynamics in Romantic Relationships. IIASA Working Paper. IIASA, Laxenburg, Austria: WP-96-074 document_url: https://pure.iiasa.ac.at/id/eprint/4953/1/WP-96-074.pdf