Feature inheritance in tree-type maps: Achieving extreme multistability and high-complexity dynamics

Existing methods for constructing chaotic systems struggle to balance dynamic complexity, feature controllability, and structural scalability, which limits the actual performance. This paper proposes two types of tree-type maps: CPCTM (Cascade-Parallel Coupling Tree-type Map) and PCCTM (Parameter-Controlled Coupling Tree-type Map). Their core innovation lies in their hierarchical tree structure. CPCTM boosts feature inheritance and complexity by leveraging the multi-level cascading-parallel coupling of seed maps, while PCCTM utilizes memristor outputs as control parameters to dynamically regulate system dynamics. Theoretical analysis demonstrates that both maps inherit the initial-boosted extreme multistability of the seed maps and exhibit inherent 2π periodicity. Performance evaluations verify that the proposed maps outperform existing models in spectral entropy, C0 complexity, and overall performance. Hardware experiments conducted on STM32 platform validate the numerical simulations. Moreover, pseudo-random sequences generated by these maps pass the NIST SP800-22 test suite, confirming their reliability for cryptographic applications.