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Published on: March 1, 2017
On the Dynamical Interplay of Positive and Negative Affects
Jonathan Touboul1, Alberto Romagnoni2, Robert Schwartz3
1Mathematical Neuroscience Team, CIRB, Collège de France, 75005 Paris, France, and Mycenae Team, Inria Paris, 75012 Paris, France jonathan.touboul@college-de-france.fr.
This study models emotional disorders using mathematical equations to understand affect balance. Findings suggest that evaluating emotions historically, not just presently, aids in recovery and resilience.
Area of Science:
- Psychology
- Mathematical Modeling
- Affective Science
Background:
- Emotional disorders arise from complex interactions between positive and negative affects.
- These interactions are influenced by external events and internal representations.
- Understanding affect balance is crucial for psychological flourishing and mental health.
Purpose of the Study:
- To mathematically model the dynamical balance between positive and negative affects.
- To investigate the impact of different therapies on affect balance.
- To provide a theoretical framework for studying emotional change and resilience.
Main Methods:
- Developed a mathematical model using delay differential equations.
- Analyzed the system's bifurcation diagram.
- Compared model predictions with psychological data from a patient undergoing therapy.
Main Results:
- The model predicts that evaluating emotional state historically promotes stabilization.
- Therapeutic interventions (coping-focused vs. affect-focused) were analyzed for their impact on affect balance.
- The study identified parameters influencing resilience to relapse.
Conclusions:
- A mathematical model can elucidate the dynamics of emotional disorders.
- Historical emotional state evaluation is key for stable emotional functioning.
- The proposed model offers insights into temporal processes of change and relapse prevention.
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