Broaden-and-Build: Upward & Downward Emotional Spirals (2D)

This is the phase-portrait counterpart to the 3D particle-cloud simulator of the same theory. It integrates the identical coupled feedback loop between positive emotion and psychological resources as an explicit two-variable nonlinear ODE, plotted live on an E–R phase plane alongside time-series traces of both variables. Because resources feed forward into future positive emotion and positive emotion feeds forward into resources, the system exhibits genuine bistability: set the initial conditions, dial in chronic stress or a broadening practice, and fire a stressor to see the exact same equations settle into a self-sustaining upward spiral of rising emotion and resources, or collapse into a downward spiral — with the vector field and nullclines on the plot showing the real flow that produces it, not a scripted animation.