Designing multi-cavity chaotic maps via multistage step state extension

Finding a generic method for designing multi-cavity chaotic maps (MCCMs) has been challenging. In this paper, we propose a generic method of multistage step state extension (MSSE) for designing MCCMs. This method is simple and effective to generate various line/grid multi-cavity chaotic attractors (MCCAs). Taking symmetric chaotic maps as seed maps, our method can be applied to construct different MCCMs using 1-D and 2-D MSSE controllers. Using this method, we construct two line/grid MCCMs with the existing parabolic chaotic map and sine/cosine modulation map as examples. The results show that MCCMs not only produce line/grid MCCAs, but also provide line/grid initial-offset boosting attractors (IOBAs). Particularly, the chaotic sequences obtained from these MCCMs have higher performance indicators than those from the seed chaotic maps. Besides, we fabricate an STM32 hardware platform to implement MCCMs, thus verifying the effectiveness of the generic method and the accuracy of the numerical results.