With increasing computing demands, serial processing in von Neumann architectures built with zeroth-order complexity digital circuits is saturating in computational capacity and power, entailing research into alternative paradigms. Brain-inspired systems built with memristors are attractive owing to their large parallelism, low energy consumption, and high error tolerance. However, most demonstrations have thus far only mimicked primitive lower-order biological complexities using devices with first-order dynamics. Memristors with higher-order complexities are predicted to solve problems that would otherwise require increasingly elaborate circuits, but no generic design rules exist. Here, we present second-order dynamics in halide perovskite memristive diodes (memdiodes) that enable Bienenstock-Cooper-Munro learning rules capturing both timing- and rate-based plasticity. A triplet spike timing-dependent plasticity scheme exploiting ion migration, back diffusion, and modulable Schottky barriers establishes general design rules for realizing higher-order memristors. This higher order enables complex binocular orientation selectivity in neural networks exploiting the intrinsic physics of the devices, without the need for complicated circuitry.