Design and FPGA implementation of a hyperchaotic conservative circuit with initial offset-boosting and transient transition behavior based on memcapacitor

A charge-controlled memcapacitive conservative chaotic circuit with trigonometric function terms is constructed in this paper. By analyzing the characteristics of the infinite equilibrium point and the divergence of the system, it is proved that the system is conservative. Under the influence of system parameters, hyperchaotic and chaotic characteristics can be switched to each other. With the increase of parameters and initial values, the Lyapunov exponent is also greatly improved. In addition, the transient chaos phenomenon accompanied by the internal crisis is also found, which leads to the sudden change of the orbit state of the attractor, and different types of coexisting attractors in different regions of the basins are also found. Through further analysis of the phase diagram, bifurcation diagram and time-domain waveform, it is found that there are three initial offset-boosting behaviors with different characteristics in the system. Finally, the spectral entropy (SE) algorithm is used to compare the memcapacitive circuit complexity under different initial conditions and system parameters. We find that the SE complexity distribution map is consistent with the Lyapunov exponent trajectory, which further reflects the influence of system parameters and initial conditions on the dynamic characteristics of the system. On the platform of Cyclone IV E series, the FPGA main chip of EP4CE10F17C8N is used to complete the hardware implementation of the system. The FPGA implementation results are consistent with numerical simulation, and verify the realistic feasibility of the memcapacitive conservative chaotic circuit in practical application.