Construction method and circuit design of a high-dimensional conservative chaotic system with binary linear combinations

The conservative chaotic system without attractor can not be reconstructed by the attractor reconstruction, which has certain advantages in the field of computer network security compared to dissipative systems. In addition, high-dimensional conservative chaotic systems have strong hyperchaotic characteristics, and less attention has been paid to the construction methods of high-dimensional conservative chaotic systems. Therefore, an effective method for constructing high-dimensional conservative chaotic systems with skew-symmetric matrices is proposed in this paper. The equation is rigid body Euler equation of bivariate product, so it is proved mathematically that the system constructed by this method satisfies the conservation of Casimir energy and Hamiltonian energy. This method can construct Hamiltonian conservative chaotic systems with different dimensions. To verify the correctness of the method, Hamiltonian conservative chaotic systems of 4D, 5D, and 6D are designed. The chaotic systems constructed by this method all exhibit the coexistence of chaotic orbits, and the orbit area increases with the increase of initial values. Interestingly, the 5D Hamiltonian conservative system we constructed has a wide range of parameter and a large initial value interval when it is in a hyperchaotic state, and the system has a strong traversal, which is verified by the Poincaré map. Finally, the NIST test, analog circuit simulation, and DSP hardware platform implementation further show that the system has good pseudo-randomness and physical realizability, and can be well applied in the field of information security and simulation of physical systems.