The collapse of Silicon Valley Bank in March 2023 unfolded in forty-eight hours, following months of visible but apparently tolerated balance-sheet deterioration. This pattern, prolonged stability followed by sudden and discontinuous collapse, is difficult to reconcile with the canonical Diamond-Dybvig model of bank runs, which treats a bank failure as an instantaneous jump between two static states. This paper proposes a dynamical systems extension of the Diamond-Dybvig framework. We model the joint evolution of depositor beliefs and bank fragility as a coupled pair of nonlinear differential equations, map the full geometry of the system, and establish two threshold results: a saddle-node bifurcation at a critical interest rate r*, at which the system changes from having one possible resting state to having two, and a Hopf bifurcation at r** > r*, at which the calm resting state loses stability and a self-sustaining oscillation appears. That oscillation formalizes the idea of a bank in chronic stress: repeatedly approaching, but not yet crossing, the edge of collapse. Therefore, a bank failure is reinterpreted not as a choice between equilibria but as the crossing of a tipping line in the space of possible states. We apply the framework to Silicon Valley Bank, arguing that the Federal Reserve’s 2022 to 2023 hiking cycle pushed the bank past the saddle-node threshold, that the ensuing months of intermittent stress correspond to the oscillatory regime, and that the capital-raise announcement of March 8th, 2023 was the discrete shock to beliefs that pushed the system across the tipping line into irreversible collapse. Policy implications for deposit insurance design, capital requirements, and depositor-network regulation follow directly from the geometry.