Modeling, Synchronization, and FPGA Implementation of Hamiltonian Conservative Hyperchaos

Conservative chaotic systems have potentials in engineering application because of their superiority over the dissipative systems in terms of ergodicity and integer dimension. In this paper, five-dimension Euler equations are constructed by integrating two of sub-Euler equations, which are contributory to the exploration of higher-dimensional systems. These Euler equations compose the conservative parts from their antisymmetric structure, which have been proved to be both Hamiltonian and Casimir energy conservative. Furthermore, a family of Hamiltonian conservative hyperchaotic systems are proposed by breaking the conservation of Casimir energy. The numerical analysis shows that the system displays some interesting behaviors, such as the coexistence of quasi-periodic, chaotic, and hyperchaotic behaviors. Adaptive synchronization method is used to realize the hyperchaos synchronization. Finally, the system passed the NIST tests successfully. Field programmable gate array (FPGA) platform is used to implement the proposed Hamiltonian conservative hyperchaos.