Design and FPGA Implementation of Grid-Scroll Hamiltonian Conservative Chaotic Flows With a Line Equilibrium

• Published in: IEEE transactions on very large scale integration (VLSI) systems Vol. 32; no. 4; pp. 658 - 668
• Main Authors: Ji'e, Musha, Peng, Hongxin, Duan, Shukai, Wang, Lidan, Zhang, Fengqing, Yan, Dengwei
• Format: Journal Article
• Language: English
• Published: New York IEEE 01.04.2024; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Behavioral sciences; Chaos theory; Chaotic communication; Conservative chaos; Controllability; controlled multiscroll flow; Field programmable gate arrays; FPGA hardware experiment; Hamiltonian functions; Hamiltonian gradient; Hessian matrix; initial offset-boosted behavior; Linear functions; Memristors; Pseudorandom; Resists; System effectiveness; Topology; Trigonometric functions; Very large scale integration
• ISSN: 1063-8210; 1557-9999
• DOI: 10.1109/TVLSI.2024.3361889

Although multiscroll attractors in dissipative chaotic systems (DCSs) have complex properties, they may be subject to reconstruction attacks in the field of information security. Conservative chaotic systems (CCSs) have no attractors and can effectively resist this danger. To obtain grid-scroll conservative chaotic flows with complex dynamical behaviors, this article proposes a symmetric sine function constrained by piecewise linear functions (Sin-PLF). Then, a 4-D Hamiltonian conservative chaotic system (HCCS) with line equilibrium and grid-scroll chaotic flows is presented by replacing the state variables with the Sin-PLF. Single-, two-, and three-directional controllable multiscroll chaotic flows are found in the system, and the stationary points of the Hamiltonian function are used to analyze the generation mechanism of these scrolls. Besides, the initial offset-boosted behavior is also found, which generates coexisting chaotic flows and coexisting quasiperiodic flows in single-, two-, and three-directions. Based on the FPGA board, the multiscroll chaotic flows in the 4-D HCCS are acquired experimentally to verify their feasibility. Finally, potential applications of the proposed grid-scroll CCS are shown through a simple pseudorandom number generator (PRNG).