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Conservative systems have no attractors. Therefore, compared with common dissipative systems, conservative systems have good ergodicity, strong pseudo-randomness and high security performance, thereby making them more suitable for applications in chaotic secure communication and other fields. Owing to these features, a new five-dimensional conservative hyperchaotic system with a wide parameter range is designed. Firstly, the Hamiltonian energy and Casimir energy are analyzed, showing that the new system satisfies the Hamiltonian energy conservation and can generate chaos. Next, the dynamic analysis is carried out, including conservativeness proof, equilibrium point analysis, Lyapunov exponential spectrum, and bifurcation diagrams analysis, thereby proving that the new system has the characteristics of conservative system and can always maintain a hyperchaotic state in a wide parameter range. At the same time, the phase diagram and Poincaré section diagram of the new system in a wide parameter range are compared. The results show that the randomness and ergodicity of the system are enhanced with the increase of parameters. Then, the NIST test shows that the chaotic random sequences generated by the new system in a wide parameter range have strong pseudo-randomness. Finally, the circuit simulation and hardware circuit experiment of the conservative hyperchaotic system are carried out, which proves that the new system has good ergodicity and realizability.
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系统 平衡点($ {k_1}, {k_4} \in \mathbb{R} $) 特征值($ \sigma , \omega \in {\mathbb{R}^ + } $) 平衡点类型 $\varSigma _1^{\rm{H} }$ $ (0, 0, 0, 0, 0) $ $ (0, {\rm{j}}{\omega _1}, - {\rm{j}}{\omega _1}, {\rm{j}}{\omega _2}, - {\rm{j}}{\omega _2}) $ 中心点 $ (0, {\sigma _1}, - {\sigma _2}, {\sigma _3} + {\rm{j}}\omega , {\sigma _3} - {\rm{j}}\omega ) $ 鞍焦点 $ ({k_1}, 0, 0, 0, 0) $ $ (0, {\sigma _1}, - {\sigma _2}, - {\sigma _3} + {\rm{j}}\omega , - {\sigma _3} - {\rm{j}}\omega ) $ 鞍焦点 $ (0, \sigma + {\rm{j}}{\omega _1}, \sigma - {\rm{j}}{\omega _1}, - \sigma + {\rm{j}}{\omega _2}, - \sigma - {\rm{j}}{\omega _2}) $ 鞍焦点 $ (0, {\sigma _1}, {\sigma _2}, - {\sigma _3}, - {\sigma _4}) $ 鞍焦点 $ (\sqrt 2 , 0, \sqrt 2 {k_4}, {k_4}, 0) $ $ (0, 0, - {\sigma _1}, {\sigma _2} + {\rm{j}}\omega , {\sigma _2} - {\rm{j}}\omega ) $ 鞍焦点 $ (0, \sigma + {\rm{j}}{\omega _1}, \sigma - {\rm{j}}{\omega _1}, - \sigma + {\rm{j}}{\omega _2}, - \sigma - {\rm{j}}{\omega _2}) $ 鞍焦点 $ (0, {\sigma _1}, {\sigma _2}, - {\sigma _3}, - {\sigma _4}) $ 鞍焦点 $ ( - \sqrt 2 , 0, - \sqrt 2 {k_4}, {k_4}, 0) $ $ (0, 0, {\sigma _1}, - {\sigma _2} + {\rm{j}}\omega , - {\sigma _2} - {\rm{j}}\omega ) $ 鞍焦点 $ (0, \sigma + {\rm{j}}{\omega _1}, \sigma - {\rm{j}}{\omega _1}, - \sigma + {\rm{j}}{\omega _2}, - \sigma - {\rm{j}}{\omega _2}) $ 鞍焦点 
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No. Statistical test P-value Proportion 1 Frequency 0.759756 0.99 2 Block frequency 0.494392 1.00 3 Cumulative sums 0.595549 1.00 4 Runs 0.867692 0.99 5 Longest run 0.102526 0.98 6 Rank 0.115387 1.00 7 FFT 0.455937 1.00 8 Nonoverlapping template 0.015598 0.98 9 Overlapping template 0.699313 0.99 10 Universal 0.678686 0.98 11 Approximate entropy 0.574903 1.00 12 Random excursions 0.186566 0.9836 13 Random excursions variant 0.023812 1.00 14 Serial 0.514124 0.99 15 Linear complexity 0.350485 0.99 DownLoad:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]
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