Modeling Complex Dynamics via Extended PWL-Based CNNs

In this paper a new strategy is proposed in order to extend the class of complex and chaotic dynamics which can be generated by a State-Controlled CNN (SC-CNN). It is shown that, with slight modifications to the original paradigm, it is possible to represent a wide class of nonlinearities by using only piecewise linear (PWL) nonlinearities as output functions of the CNN. The adopted circuitry is presented, together with several examples concerning the emulation of the Rossler and Lorenz chaotic systems, and the Partial Differential Equations (PDE) governing the complex phenomena of solitons (Korteweg-de Vries PDE) and the activator-inhibitor reaction for the formation of patterns in the sea shells (Meinhardt-Gierer PDE). The results achieved enforce the role of SC-CNNs as universal paradigm for the generation of nonlinear, complex dynamics.