From homogeneity to heterogeneity: Topologically reconfigurable multi-cavity attractors in memristive chaotic maps

In recent years, multi-cavity attractors have emerged as a focal point in chaotic dynamics research. However, previous studies have predominantly focused on homogeneous multi-cavity attractors, where all cavities share identical topological structures. While topologically interesting, this homogeneity leads to highly similar statistical characteristics across cavities, potentially posing a threat to its cryptographic applications. To address this limitation, this study proposes a concise chaotic map construction scheme based on discrete memristors. Mathematical analysis reveals that this map exhibits no fixed points and can stably generate hidden attractors. Crucially, by selecting periodic or aperiodic memristive functions, it is possible to construct both homogeneous and heterogeneous multistability or multi-cavity attractors. Furthermore, we demonstrate that the heterogeneous structure breaks the periodic redundancy inherent in its homogeneous counterpart, resulting in a significantly larger and scalable effective key space. This finding quantitatively validates the enhanced security potential of the proposed map in fields, such as information encryption. This research not only expands the conceptual boundaries of multi-cavity attractors in chaotic systems but also presents a promising novel framework for diverse engineering applications.