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The Kuroshio Extension (KE) flow in the North Pacific Ocean displays a very distinctive decadal variability of bimodal character involving two completely different states (a large-meander “elongated” state and a small-meander “contracted” state) connected by very asymmetric temporal transitions. Although such a flow has been widely studied by means of a suite of mathematical models and by using several observational platforms, a satisfactory theoretical framework answering quite elementary questions is still lacking, the main question being whether such variability is induced by a time-varying wind forcing or, rather, by intrinsic oceanic mechanisms. In this context, the chaotic relaxation oscillation produced by a process-oriented model of the KE low-frequency variability, with steady climatological wind forcing, was recently recognized to be in substantial agreement with altimeter data. Here those model results are further compared with a comprehensive altimeter dataset. The positive result of such a comparison allows the conclusion that a minimal model for the KE bimodality has been identified and that, consequently, nonlinear intrinsic oceanic mechanisms are likely to be the main cause of the observed variability. By applying the methods of nonlinear dynamical systems theory, relevant dynamical features of the modeled flow are then explained, such as the origin of the relaxation oscillation as a consequence of a homoclinic bifurcation, the spatiotemporal character of the bimodal behavior, and the degree of predictability of the flow in the different stages of the oscillation (evaluated through a field of finite-time Lyapunov exponents and the corresponding Lagrangian time series). [ABSTRACT FROM AUTHOR]