A new three-dimensional conservative system with non - Hamiltonian energy and its synchronization application

In this paper, a three-dimensional conservative system is proposed. By analyzing the Hamiltonian energy, it is concluded that it is a non-Hamiltonian conservative system. By changing the values of the parameters b, c, the system presents different attractors. Then, by studying the multiple attractors coexisting of the system under different initial values, it can be found that the system has rich coexistence phenomena by changing the parameters. There are various types of coexistence of systems with chaos and chaos coexistence, periods and periods coexistence and chaos and periods coexistence. In addition, the offset-boosting under parameter control is studied by phase diagram. By studying the complexity of the system at two different initial values, the more complex initial value is chosen as the initial state when the system is synchronized. The analog simulation circuit is implemented using Multisim, the actual digital circuit is implemented with field programmable gate array (FPGA). The Matlab phase diagram, the numerical simulation results and the simulated circuit all agree well, proving the feasibility of the new system. Finally, the system is applied to backstepping synchronization, which lays a foundation for the realization of engineering application.

Automated summary

In this paper, a three-dimensional conservative system is proposed and analyzed, showing that it is a non-Hamiltonian system. Different attractors are observed by changing the values of the system parameters, indicating rich coexistence phenomena. The complexity of the system is studied to determine the optimal initial state for synchronization. The system is successfully implemented in analog and digital circuits, proving its feasibility. Finally, the system is applied to backstepping synchronization, paving the way for engineering applications.