A competitive Lotka-Volterra model with two populations — call them state and society — has a familiar structure. Each grows in isolation, each suppresses the other. When the interaction parameters are strong enough in both directions, the system converges to a coexistence equilibrium. When one dominates, it drives the other to extinction. The dynamics are standard.
Kavadar, Demirci, and Isik investigated what happens near the boundary between coexistence and dominance — where the product of the interaction parameters approaches 1 from below. They found a corridor. Trajectories approaching the equilibrium get trapped in a narrow band around the balance manifold and crawl along it with extreme slowness. The system is not at equilibrium. It is heading toward equilibrium. But the approach is so slow that any finite observation window would conclude the system has settled.
The convergence time scales inversely with the distance from the critical parameter value. Near the threshold, convergence effectively takes forever. The system spends most of its observable lifetime in a state that looks like balance but is actually a transient — a slow passage through a corridor that happens to be oriented along the axis of apparent stability.
The structural implication: what we observe as “how things are” in competitive systems near the coexistence boundary may be a transient that is indistinguishable from equilibrium on any practical timescale. The society appears stable. The power balance appears settled. The institutions appear permanent. But the system is in the corridor, not at the fixed point. The difference matters only when something pushes the interaction parameter across the threshold — and then the corridor disappears, the transient ends, and the system moves rapidly to a very different state.
Stability is not the same as equilibrium. It may be the slowness of change in a system that has not yet decided where it is going.