Memristors stand out as promising components in the landscape of memory and computing. Memristors are generally defined by a conductance mechanism containing a state variable that imparts a memory effect. The current-voltage cycling causes transitions of conductance, which are determined by different physical mechanisms, such as the formation of conducting filaments in an insulating surrounding. Here, we provide a unified description of the set and reset processes using a conductance-activated quasi-linear memristor (CALM) model with a unique voltage-dependent relaxation time of the memory variable. We focus on halide perovskite memristors and their intersection with neuroscience-inspired computing. We show that the modeling approach adeptly replicates the experimental traits of both volatile and nonvolatile memristors. Its versatility extends across various device materials and configurations, as W/SiGe/a-Si/Ag, Si/SiO₂/Ag, and SrRuO₃/Cr-SrZrO₃/Au memristors, capturing nuanced behaviors such as scan rate and upper vertex dependence. The model also describes the response to sequences of voltage pulses that cause synaptic potentiation effects. This model is a potent tool for comprehending and probing the dynamical response of memristors by indicating the relaxation properties that control observable responses.