Memristors are candidate devices for constructing artificial neurons, synapses, and computational networks for brainlike information processing and sensory-motor autonomous systems. However, the dynamics of natural neurons and synapses are challenging and cannot be well reproduced with standard electronic components. Halide perovskite memristors operate by mixed ionic-electronic properties that may lead to replicate the live computation elements. Here we explore the dynamical behavior of a halide perovskite memristor model to evaluate the response to a step perturbation and the self-sustained oscillations that produce analog neuron spiking. As the system contains a capacitor and a voltage-dependent chemical inductor, it can mimic an action potential in response to a square current pulse. Furthermore, we discover a property that cannot occur in the standard two-dimensional model systems: a three-dimensional model shows a dynamical instability that produces a spiking regime without the need for an intrinsic negative resistance. These results open a new pathway to create spiking neurons without the support of electronic circuits.