Research And FPGA Implementation Of Multi-Scroll Hamiltonian Conservative Chaotic Systems

Chaos exists widely in nature as a kind of nonlinear dynamic,and has attracted a lot of attention from researchers.Especially in recent years,the research on characteristics of conservative chaos in nonlinear systems is becoming a new focus.Compared with dissipative chaotic systems,conservative chaotic systems have some significant characteristics,for example,the sum of Lyapunov index is zero,divergence is zero,dimension is integer dimension,ergodicity is good,probability density curve of chaotic sequence is relatively stable and similar to uniformly distributed white noise,etc.Due to these characteristics of conservative chaos,it is more suitable for application in secure communication.This paper studies generalized Hamiltonian conservative systems,and the main innovative work is as follows:(1)For two generalized Hamiltonian chaotic systems with complex dynamics: a generalized Hamiltonian conservative chaotic system with multi-stable flows and a generalized Hamiltonian chaotic system with transient quasi-periodic flows and intermittent chaotic flows,which are only verified from the perspective of numerical analysis,the paper further utilizes FPGA technology to prove them physically.Coexistence characteristics of chaotic flows,quasi-periodic flows and periodic flows in two generalized Hamiltonian chaotic systems are all observed by oscilloscope to be consistent with the numerical analysis results.In addition,transient quasi-periodic flow in one of them was observed by oscilloscope.All experimental results show that results of FPGA implementation are consistent with those of numerical simulation.(2)By extending the equilibrium points of a generalized Hamiltonian conservative chaotic system,scrolls and bonds are generated at the equilibrium points of the generalized Hamiltonian conservative chaotic system to form the multi-scroll conservative chaotic flows,and multi-scroll conservative chaotic systems are obtained.At the same time,the direction and number of multi-scroll conservative chaotic flows can be controlled by controlling the direction and number of equilibrium points.In addition,multi-scroll conservative chaotic systems can also be constructed based on the Hamiltonian energy,that is,multi-scroll conservative chaotic systems are obtained by changing the Hamiltonian energy’s invariant surface of a generalized Hamiltonian chaotic system.The NIST test of multi-scroll conservative chaotic systems shows that their pseudo-randomness is better than that of the general non-multi-scroll conservative chaotic systems and better with the increase of the number of scrolls.(3)The periodic module,the normalized module and the Taylor expansion module are designed to get the sinusoidal approximate value of the signal x in the multi-scroll conservative chaotic system,and then multi-scroll conservative chaotic systems are realized by FPGA technology.The experimental results show that FPGA implementation of multiscroll conservative chaotic systems is consistent with numerical analysis,which verifies physical realizability of multi-scroll conservative chaotic systems and provides new physical models for application.