Abstract
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.
Highlights
Since the discovery of Lorenz attractor in 1963 [1], the interesting dynamic behavior of chaotic attractors has attracted intensive attention, with various mathematical analyses
Conventional analyses on the chaotic system include the determination of Lyapunov exponents (LEs), bifurcation diagram [2], phase portrait, ultimate boundary estimation, and topological horseshoe analysis [3, 4], which illustrate the chaotic state intuitively
LEs are commonly used as an indicator of chaotic systems. e bifurcation diagram focuses on the evolution of the dynamics of a chaotic system when parameters or initial values are changed. e phase portrait describes the phase space trajectory of a chaotic system. e ultimate boundary estimation and topological horseshoe analysis [3, 4] reveal the abundant characteristics of a chaotic system
Summary
Since the discovery of Lorenz attractor in 1963 [1], the interesting dynamic behavior of chaotic attractors has attracted intensive attention, with various mathematical analyses. In research of chaotic systems, an important and useful implementation is encryption algorithms [13,14,15,16] because of the complex properties, such as extremely sensitive dependency on initial conditions, topologically mixing and density of periodic orbits, broadband, pseudo-randomness, and white-noise-like phenomenon [16]. E rest of this paper is listed as follows: in Section 2, five 5D Euler equations are constructed, and a family of HCCSs are proposed; in Section 3, the nonconservation property of the proposed HCCS and dynamics are analyzed in detail by numerical simulation; in Section 4, adaptive synchronization is achieved for system ΣH3 ; in Section 5, FPGA digital development platform is used to generate the pseudo-random number generator; and Section 6 concludes the paper
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