An excitable membrane is a semipermeable membrane whose ionic conductances or, equivalently, ionic permeabilities are sensitive to the voltage across the membrane (or membrane potential). At appropriate conditions, such membranes may amplify perturbations of the membrane potential and may trigger stereotypical voltage trajectories such as action potentials, oscillations, or bursting in several types of cells such as neurons, myocytes, and electrocytes.

The diffusion of ions across a semipermeable membrane drives the membrane potential toward its equilibrium potential, which depends upon the temperature, ionic concentrations, and the relative permeabilities of the ions, as described by the Goldman equation. When the membrane contains voltage-gated ion channels, the ionic conductances change in response to changes in the membrane potential. The instantaneous equilibrium potential then also changes continually. Changes in membrane conductance also produce proportional changes in the time constant of the membrane, affecting the rate of change of the membrane potential. This nonlinear interaction between the membrane potential and the ionic conductances constitutes a nonlinear dynamical system. In some states (e.g. the threshold potential) excitable membranes can amplify perturbations from a steady-state condition by positive feedback or dampen perturbations by negative feedback and generate stereotyped trajectories (attractors). For example, action potentials in a neuron have similar amplitude and shape independently of the amplitude of the stimulus that initiated it.

A successful model of an excitable membrane is the Hodgkin–Huxley model. The model accurately describes the dynamics of the voltage across an excitable membrane containing two populations of voltage-gated channels and helped explain the nature of action potentials. The great diversity of voltage-gated channels and their densities in cell membranes help explain the great variety and complexity of excitable cell properties.