CBD Formula – Crowd Behavior Dynamics

Formule CBD – Comportement et Dynamique de la Foule_Diaphragme.pdf

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CBD Formula – Crowd Behavior Dynamics_Diaphragme.pdf

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The CBD formula is a theoretical framework for modeling collective behavior in crowds, financial markets, and social systems, showing how complexity emerges from nonlinear local interactions without central control.

It is based on fundamental variables (S, R, V, D, C, M, T, I) that interact at three levels: infinitesimal (initial conditions), intermediate (nonlinear dynamics with feedback and bifurcations), and macroscopic (observable phenomena such as bubbles or social movements).

The psychodynamic potential ψ represents a landscape of stable attractors (S) and barriers (R), where transitions occur through critical windows O(t) × D(t) and a final filter F(t).

The mathematical formula P(t) = A · ψ × [O(t) × D(t)] × F(t) quantifies the observable output, illustrated by landscape diagrams and multi-level emergence representations.

Applications include financial markets and crowd simulations, with limitations related to sensitivity to initial conditions, and it integrates theories such as René Thom’s catastrophe theory.