Hierarchical regulation of scroll capacity and attractor connectivity in memristive chaotic systems

The key challenge in multiscroll chaos is to regulate scroll capacity and attractor connectivity within a unified framework. This study develops an offset-boosted memristor and incorporates it into several offset-controllable oscillators through a unified coupling scheme, demonstrating the transferability of the proposed mechanism across different dynamical structures. Successive offset-doubling operations progressively expand the scroll capacity without altering the coupling architecture, while hierarchical offsets govern inner-scroll preservation and outer-scroll activation. More importantly, relative offset regulation selectively preserves or disrupts inter-scroll transition channels, enabling a fixed scroll population to be reorganized into fully connected, partially separated, or completely separated coexisting attractors. This reconfiguration further produces homogeneous and heterogeneous coexistence patterns with adjustable branch composition, spatial distribution, and inter-attractor spacing. Different coexisting branches can be selected through the initial memristive state, providing an additional degree of freedom for state organization. The proposed framework therefore enables hierarchical control of scroll capacity, attractor connectivity, and coexistence topology, with its feasibility further demonstrated by STM32-based circuit implementation.