A new four-dimensional hyperchaotic system with hidden attractors and multistablity

Abstract This paper proposes a novel 4D hyperchaotic system with hidden attractors and coexisting attractors, which have no equilibrium points. The dynamic behavior of the system and five groups of coexisting attractors are analyzed by applying phase space diagrams, bifurcation diagrams and the Lyapunov exponents spectrum. Additionally, the system’s stable limit cycles and unstable periodic orbits were calculated through the variational method and then encoded using symbolic dynamics. The numerical results were verified via a circuit simulation, confirming the realizability of the novel hyperchaotic system in hardware facilities. Finally, we applied the active synchronization control method to the new system with remarkable results.