In this paper, a novel hardware-efficient integrated cochlear model, whose nonlinear dynamics is described by ergodic sequential logics, is presented. It is shown that the presented cochlear model can reproduce combination tone generation of a mammalian cochlea, which is one of the most typical nonlinear sound processing functions of mammalian cochleae. In addition, the presented model is implemented by a field-programmable gate array (FPGA) and its operations are verified by experiments. It is then shown that the presented model consumes much less hardware resources and much less power compared to a standard ordinary differential equation model of cochlea.