A novel design method of an integrated cochlear model, designed for hardware efficiency, is presented, where its nonlinear dynamics is governed by ergodic sequential logic. It is shown the presented model can reproduce the nonlinear compression characteristics of a mammalian cochlea, which is one of the most representative mammalian nonlinear sound processing functions. Furthermore, the presented model is implemented by a field-programmable gate array and its functionality is confirmed through experiments. It is shown the presented model consumes significantly lower hardware resources and power in comparison to a standard ordinary differential equation cochlear model.