Multi-scroll Hamiltonian conservative chaotic and hyperchaotic flows based on integrated 4D Euler equations

The paper first proposes novel multi-scroll Hamiltonian conservative chaotic and hyperchaotic systems (CCHSs) by investigating a class of generalized Hamiltonian conservative chaotic systems (CCSs) based on integrated 4D Euler equations. The proposed multi-scroll Hamiltonian CCHSs can generate a tunable number of multi-scroll flows along all four directions, either in a combined or independent manner. The novelty of the proposed systems lies in that multi-scroll dynamics are not consistently observed, instead, dynamics with different scrolls are identified. Subsequently, numerical analysis are given to show the complex dynamical behaviors inherent to the proposed multi-scroll Hamiltonian CCHSs. Moreover, hyperchaotic behaviors are further uncovered during the investigation of multi-scroll dynamical characteristics. Finally, field-programmable gate array (FPGA) circuits are adopted to physically implement the proposed multi-scroll Hamiltonian CCHSs, which not only verify the existence of multi-scroll Hamiltonian conservative chaotic and hyperchaotic dynamics experimentally but also provide novel physical models for practical chaos-related applications.