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Rupture styles emerge in a broad range of rupture styles, from slow-slip events collocated with or without tremors to pulse-like earthquake sequences. Meanwhile, Earthquake catalogs exhibit various recurrence patterns, from periodic and characteristic earthquakes to chaotic sequences with super-cycles, aftershocks and dissimilar ruptures. The underlying physical mechanisms of these phenomena are usually documented separately and the potential connection between them is poorly understood. Here, we explore a wide range of frictional properties using quasi-dynamic models of seismic cycles in two dimension to assess the link between rupture style and recurrence patterns. We obtain a broad spectrum of rupture behaviors controlled by several non-dimensional parameters, including the Dieterich-Ruina-Rice number Ru, which is the ratio of asperity to a characteristic nucleation size, and Rb, which reflects the relative amplitude of weakening and strengthening effects. Seismogenic slow-slip events are the natural behavior of near-velocity neutral condition (low Rb) with a small characteristic nucleation size (high Ru), which is commonly found below the seismogenic zone. The deviation from periodic and characteristic recurrence behaviors are responses of homogeneous or compliant fault-zone models with high Ru numbers. The presence of a compliant zone can be incorporated into the Ru number in quasi-dynamic simulations. Observations of rupture characteristics and recurrence patterns can bring useful constraints on the physical properties of fault zones.