We propose a new overarching model for self-propelled particles that flexibly generates a full family of "descendants." The general dynamics introduced in this paper, which we denote as the "parental" active model (PAM), unifies two special cases commonly used to describe active matter, namely, active Brownian particles (ABPs) and active Ornstein-Uhlenbeck particles (AOUPs). We thereby document the existence of a deep and close stochastic relationship between them, resulting in the subtle balance between fluctuations in the magnitude and direction of the self-propulsion velocity. Besides illustrating the relation between these two common models, the PAM can generate additional offsprings, interpolating between ABP and AOUP dynamics, that could provide more suitable models for a large class of living and inanimate active matter systems, possessing characteristic distributions of their self-propulsion velocity. Our general model is evaluated in the presence of a harmonic external confinement. For this reference example, we present a two-state phase diagram that sheds light on the transition in the shape of the positional density distribution from a unimodal Gaussian for AOUPs to a Mexican-hat-like profile for ABPs. Published under an exclusive license by AIP Publishing.
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