Modelling and simulation of the multi-scroll chaotic attractors using bond graph technique

This paper presents modelling and simulation of multi-scroll chaotic attractors by using a new simple and more general bond graph model. For this purpose, the multi-segment non-linear resistor in Chua's circuit is modelled by using piecewise linearization with control inequalities. The proposed model consists of active/passive circuit elements, voltage-controlled current source (VCCS) and ideal switches. The advantage of modelling multi-segment non-linear resistor by using control inequalities yields minimum number of the switches and sources. Proposed model is simple and more general and, especially, could be used in various kinds of non-linear circuit in the chaos studies. Generally, two different non-linear resistor models are used in the literature to obtain odd and even numbers of the scrolls. In this study, one model is developed for both multi-scroll chaotic attractors. In this paper, bond graph simulation of Chua's circuit is realized by using proposed model. The BONDAS program that developed in Matlab is used for the simulations, and satisfactory results are obtained.