Piecewise linear implementation of nonlinear dynamical systems: from theory to practice

It is shown how to implement by a mixed-signal circuit a continuous-time dynamical system. The chosen case study is the Hindmarsh-Rose model of a biological neuron, but the design strategy can be applied to a large class of continuous-time nonlinear dynamical systems. The system nonlinearities are first approximated by using piecewise-linear functions and then digitally implemented on a field programmable gate array. The linear part of the system is completely analogue and is implemented by using operational amplifiers. Measurement results show that the circuit can reproduce the main dynamics of a biologically plausible neuron.