Dynamical analysis, circuit realization, and applications of 4D hyperchaotic systems with bursty oscillations and infinite attractor coexistence

A new four-dimensional chaotic system with high complexity is proposed, and the analysis of its dynamics reveals that the system shows a rare topological attractor structure symmetry phenomenon. The phenomenon of inverse multiplicative bifurcation and multistability, which changes from a quadruple period to a double period and then to a single period, are found. A complex oscillatory transformation between chaos and period can be observed, highlighting the complexity of the system. The transient hyperchaos and burst oscillations are found in the time series and Lyapunov exponential spectra of the system, and the rich dynamical behavior of the system is verified by the 0–1 test and complexity spectral entropy test. The analog circuitry of the system is simulated based on Multisim, and the actual digital circuitry of the system is implemented through a Field Programmable Gate Array. The experimental results and the numerical simulation results agree and prove the feasibility of the constructed system. An image encryption algorithm is designed by combining the disruption-diffusion algorithm with the DNA encoding algorithm, and the system is analyzed and verified to be highly sensitive to the chaotic sequence key and initial value. Moreover, the key space of the algorithm is large and the information entropy is close to the ideal value, so the new system proposed can contribute to play a role in the field of secure communication.