Synthesis of PWL Functions

The design of a nonlinear function with multi-segments is a basis for generating chaotic attractors with multidirectional orientation and with a large number of scrolls. However, it has been identified that it is quite difficult to synthesize nonlinear functions with multi-segments by using analog electronic circuits. Therefore, to cope with this problem, the electronic design automation (EDA) industry is developing design tools with a high degree of abstraction (behavioural modelling). Henceforth, the synthesis approach presented in this chapter depends on the behavioural modelling of the chaotic systems introduced in Chapter. 3. In particular, this approach is focused on designing multi-scrolls chaotic attractors with multidirectional orientation. In this manner, this chapter first presents a basic cell based on opamps to synthesize saturated nonlinear functions series. Further, a new synthesis approach is introduced to design the saturated functions in current and voltage modes by using a general scheme of connection for basic cells. Finally, at the end of this chapter, a Verilog-A model for considering no-ideal effects of the opamps is defined to execute SPICE simulations.

Keywords: Chaos, electronic design automation, dynamical systems, chaos generators, modelling and simulation.