The G&G Model: A Dynamic Analysis of Leadership Force Field With Multistability Approach, Attractors, and Spectral Decomposition

Source abstract

Building on Lewin’s force field theory and on the G&G model, we represent 11 leadership styles (authoritarian, participative, laissez‐faire or hands‐off, transformational, transactional, visionary, coaching, affiliative, democratic, pacesetting, and directive) as planar systems of differential equations whose state variables are the favorable and restrictive forces of the field. For each style, we determine the equilibria and classify them through the spectrum of the Jacobian matrix, using the Hartman–Grobman theorem, Lyapunov stability, and spectral decomposition; the eigenvalues distinguish saddle points from stable and unstable kernels. Phase portraits obtained with the fourth‐order Runge–Kutta method display the critical points and the trajectory flows, and the scheme is validated against the explicit Euler and Heun methods and a nonstandard finite difference scheme, in terms of order of convergence, positivity, stability, and cost. The framework clarifies the transitions between leadership styles in a socio‐organizational system and supports regulation strategies adapted to the observed states of stability.