A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution
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{"title"=>"A mathematical model of sentimental dynamics accounting for marital dissolution", "type"=>"journal", "authors"=>[{"first_name"=>"José Manuel", "last_name"=>"Rey", "scopus_author_id"=>"7401950789"}], "year"=>2010, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "pui"=>"368277914", "sgr"=>"79952118381", "doi"=>"10.1371/journal.pone.0009881", "scopus"=>"2-s2.0-79952118381", "isbn"=>"1932-6203", "pmid"=>"20360987"}, "id"=>"f1596aeb-8b6e-38f9-80fa-3d2e616a8397", "abstract"=>"BACKGROUND: Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of second law of thermodynamics for sentimental relationships. Effort is required to sustain them. Love is not enough.\\n\\nMETHODOLOGY/PRINCIPAL FINDINGS: Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics.\\n\\nCONCLUSIONS/SIGNIFICANCE: These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.", "link"=>"http://www.mendeley.com/research/mathematical-model-sentimental-dynamics-accounting-marital-dissolution", "reader_count"=>122, "reader_count_by_academic_status"=>{"Unspecified"=>2, "Professor > Associate Professor"=>13, "Librarian"=>1, "Student > Doctoral Student"=>9, "Researcher"=>31, "Student > Ph. D. Student"=>30, "Student > Postgraduate"=>7, "Student > Master"=>5, "Other"=>6, "Student > Bachelor"=>7, "Lecturer"=>4, "Professor"=>7}, "reader_count_by_user_role"=>{"Unspecified"=>2, "Professor > Associate Professor"=>13, "Librarian"=>1, "Student > Doctoral Student"=>9, "Researcher"=>31, "Student > Ph. D. Student"=>30, "Student > Postgraduate"=>7, "Student > Master"=>5, "Other"=>6, "Student > Bachelor"=>7, "Lecturer"=>4, "Professor"=>7}, "reader_count_by_subject_area"=>{"Unspecified"=>4, "Agricultural and Biological Sciences"=>32, "Business, Management and Accounting"=>1, "Chemistry"=>7, "Computer Science"=>11, "Earth and Planetary Sciences"=>1, "Engineering"=>7, "Environmental Science"=>4, "Biochemistry, Genetics and Molecular Biology"=>1, "Materials Science"=>3, "Mathematics"=>11, "Medicine and Dentistry"=>12, "Neuroscience"=>2, "Pharmacology, Toxicology and Pharmaceutical Science"=>1, "Physics and Astronomy"=>12, "Psychology"=>7, "Social Sciences"=>5, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Materials Science"=>{"Materials Science"=>3}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>12}, "Social Sciences"=>{"Social Sciences"=>5}, "Physics and Astronomy"=>{"Physics and Astronomy"=>12}, "Psychology"=>{"Psychology"=>7}, "Mathematics"=>{"Mathematics"=>11}, "Unspecified"=>{"Unspecified"=>4}, "Environmental Science"=>{"Environmental Science"=>4}, "Pharmacology, Toxicology and Pharmaceutical Science"=>{"Pharmacology, Toxicology and Pharmaceutical Science"=>1}, "Engineering"=>{"Engineering"=>7}, "Chemistry"=>{"Chemistry"=>7}, "Neuroscience"=>{"Neuroscience"=>2}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>32}, "Computer Science"=>{"Computer Science"=>11}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}}, "reader_count_by_country"=>{"Republic of Singapore"=>1, "Argentina"=>1, "Hungary"=>2, "Hong Kong"=>1, "United States"=>5, "United Kingdom"=>3, "Portugal"=>2, "Switzerland"=>1, "Spain"=>3, "Canada"=>1, "Netherlands"=>1, "Luxembourg"=>1, "Brazil"=>2, "Poland"=>1, "Mexico"=>3, "Slovakia"=>1, "France"=>3, "Chile"=>1, "Germany"=>1}, "group_count"=>6}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/855912"], "description"=>"<p>The shape of feeling utility <i>U</i> is the standard picture assumed in the social sciences. Utility from effort, represented by −<i>D</i>, increases till it reaches <i>c</i>* but decreases beyond this point. Marginal effort utility is decreasing and vanishes at <i>c</i>*. Thus −<i>D</i> is concave in shape reaching an absolute maximum at <i>c*</i>.</p>", "links"=>[], "tags"=>["shapes", "disutility"], "article_id"=>526368, "categories"=>["Mathematics", "Mental Health", "Medicine"], "users"=>["José-Manuel Rey"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0009881.g001", "stats"=>{"downloads"=>4, "page_views"=>27, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Utility_structure_typical_shapes_of_utility_and_disutility_functions_/526368", "title"=>"Utility structure: typical shapes of utility and disutility functions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-31 01:46:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/855999"], "description"=>"<p>Under the specifications of the model, there is always a unique feeling-effort equilibrium E of the optimal sentimental flow defined by Eqs. (1)–(2). This is a viable solution if <i>x</i><sub>s</sub><sup>♥</sup>><i>x</i><sub>min</sub> and the effort gap <i>c</i><sub>s</sub><sup>♥</sup>−<i>c</i>* is tolerable. The vertical nullcline (where the sentimental flow is vertical, that is ) is the line <i>ac</i> = <i>rx</i> The horizontal nullcline is the curve <i>c<sub>H</sub></i>(<i>x</i>) where the sentimental dynamics is flat, i.e. , and its graph is always decreasing and located above the line <i>c</i> = <i>c</i>*. The graph represented above corresponds to the case that <i>U</i>′(0)<+∞, in turn implying <i>c<sub>H</sub></i>(0)<+∞.</p>", "links"=>[], "tags"=>["mathematics", "mathematics/nonlinear dynamics", "mental health/psychology", "non-clinical medicine/sociology"], "article_id"=>526464, "categories"=>["Mathematics", "Mental Health", "Medicine"], "users"=>["José-Manuel Rey"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0009881.g002", "stats"=>{"downloads"=>2, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Sentimental_equilibrium_/526464", "title"=>"Sentimental equilibrium.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-31 01:47:44"}
  • {"files"=>["https://ndownloader.figshare.com/files/856082"], "description"=>"<p>Under the assumptions of the model, there is a unique effort policy that takes the initial feeling <i>x</i><sub>0</sub> to the unique equilibrium E. This is achieved by setting the initial effort at point A to get onto the stable manifold <i>W</i><sub>s</sub><sup>+</sup> and then following path AE to approach equilibrium. Trajectories starting above <i>W</i><sub>s</sub><sup>+</sup> (e.g. at point A′) are not acceptable. The target trajectory AE always lies above the line <i>c</i> = <i>c</i>*. The relationship is viable provided that the effort gap <i>c</i><sup>♥</sup>(<i>t</i>)−<i>c</i>* is tolerable along the transition to equilibrium, that must also satisfy <i>x</i><sub>s</sub><sup>♥</sup>><i>x</i><sub>min</sub>. Furthermore, since the target trajectory AE is unstable, trajectories starting at lower effort levels (e.g. at point A″) depart from AE and eventually lead to abandon effort (setting <i>c</i> = 0).</p>", "links"=>[], "tags"=>["mathematics", "mathematics/nonlinear dynamics", "mental health/psychology", "non-clinical medicine/sociology"], "article_id"=>526542, "categories"=>["Mathematics", "Mental Health", "Medicine"], "users"=>["José-Manuel Rey"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0009881.g003", "stats"=>{"downloads"=>2, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Durable_relationships_/526542", "title"=>"Durable relationships.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-31 01:49:02"}
  • {"files"=>["https://ndownloader.figshare.com/files/425612"], "description"=>"<div><h3>Background</h3><p>Marital dissolution is ubiquitous in western societies. It poses major scientific and sociological problems both in theoretical and therapeutic terms. Scholars and therapists agree on the existence of a sort of <em>second law of thermodynamics for sentimental relationships</em>. Effort is required to sustain them. Love is not enough.</p><h3>Methodology/Principal Findings</h3><p>Building on a simple version of the second law we use optimal control theory as a novel approach to model sentimental dynamics. Our analysis is consistent with sociological data. We show that, when both partners have similar emotional attributes, there is an optimal effort policy yielding a durable happy union. This policy is prey to structural destabilization resulting from a combination of two factors: there is an effort gap because the optimal policy always entails discomfort and there is a tendency to lower effort to non-sustaining levels due to the instability of the dynamics.</p><h3>Conclusions/Significance</h3><p>These mathematical facts implied by the model unveil an underlying mechanism that may explain couple disruption in real scenarios. Within this framework the apparent paradox that a union consistently planned to last forever will probably break up is explained as a mechanistic consequence of the second law.</p></div>", "links"=>[], "tags"=>["mathematical", "sentimental", "marital", "dissolution"], "article_id"=>144030, "categories"=>["Mathematics", "Mental Health", "Medicine"], "users"=>["José-Manuel Rey"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0009881", "stats"=>{"downloads"=>24, "page_views"=>15, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/A_Mathematical_Model_of_Sentimental_Dynamics_Accounting_for_Marital_Dissolution/144030", "title"=>"A Mathematical Model of Sentimental Dynamics Accounting for Marital Dissolution", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2010-03-31 01:07:10"}
  • {"files"=>["https://ndownloader.figshare.com/files/856180"], "description"=>"<p>The model produces a plausible scenario, through a sequence of effort inattentions, for the deterioration of a relationship in a gradual form, which seems to be typical according to data. Because of the effort gap, there is a tendency to lower the right effort level. Then the intrinsic instability of sentimental dynamics obeying the second law causes the piecewise decaying trajectories to move further and further away from the target trajectory and eventually to cross the threshold level <i>x</i><sub>min</sub>. This is considered a point of <i>pre-rupture</i>, since it is a matter of time before effort is abandoned.</p>", "links"=>[], "tags"=>["mathematics", "mathematics/nonlinear dynamics", "mental health/psychology", "non-clinical medicine/sociology"], "article_id"=>526645, "categories"=>["Mathematics", "Mental Health", "Medicine"], "users"=>["José-Manuel Rey"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0009881.g004", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Breakup_mechanics_/526645", "title"=>"Breakup mechanics.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2010-03-31 01:50:45"}

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