Computation of delay-free nonlinear digital filter networks. Application to chaotic circuits and intracellular signal transduction

A method for the computation of nonlinear digital filter networks containing delay-free loops is proposed. By preserving the topology of the network this method permits the inspection of all signals flowing across the loops. Furthermore, it enables to discretize analog filter networks described by nonlinear ordinary differential equation systems on a block-by-block basis, in such a way that ad hoc analog-to-digital maps can be individually applied to each filter. A nonlinear implicit system must be solved at every computation step using iterative methods, holding certain sufficient conditions for the existence of the solution. This condition is in algebraic relationship with the causality and structure of the network and its filtering blocks. The proposed method can be straightforwardly applied to the computation of several interconnected networks. This property adds modularity to the procedure, and enables to handle changes in the network topology. Examples are presented showing the applicability of the method to the computation of the Chua-Felderhoff RLC circuit and to the dynamic simulation of a known intracellular signal transduction model of circadian cycles in Drosophila melanogaster.