Project · Jul 2023

Mathematical Modeling of Idea Intrusion

This research project uses mathematical modeling to study how committed minority groups, mainstream populations, and deradicalization mechanisms can shape opinion dynamics over time.

Mathematical ModelingStability AnalysisMATLABResearch

Conceptual phase diagram for opinion dynamics model — Conceptual view of competing social forces: mainstream influence, committed minority pressure, and deradicalization effects.

Highlights

Modeled interaction dynamics between mainstream and committed minority groups
Studied stability, bifurcation behavior, and deradicalization strategies

Problem

The project explores how a committed minority can influence a larger population and under what conditions the system converges, fragments, or shifts toward a new equilibrium.

Approach

I formulated a dynamical-system model and studied equilibrium behavior under different parameter settings. Stability and bifurcation analysis helped identify how changes in influence strength or deradicalization rates alter long-term outcomes.

Defined state variables for population groups and belief states
Analyzed fixed points and local stability
Explored parameter regimes with numerical simulation

Takeaway

The work connected applied mathematics with social dynamics, showing how qualitative behavior can change sharply when influence or intervention parameters cross critical thresholds.