A New Five-Dimensional Hyperchaotic System with Six Coexisting Attractors

This article presents a hyperchaotic system of five-dimensional autonomous ODEs that has five cross-product nonlinearities. Under certain parametric conditions, it exhibits three different types of hyperchaotic and chaotic systems which correspond to six hyperchaotic attractors with a non-hyperbolic equilibrium line, four chaotic attractors with seventeen hyperbolic equilibria, and four chaotic attractors with only one hyperbolic equilibrium, respectively. The fundamental dynamics are analyzed theoretically and numerically, such as the onset of hyperchaos and chaos, routes to chaos, persistence of chaos, coexistence of attractors, periodic windows and bifurcations. It is particularly shown that the coexisting attractors of the 5D system inside the hypercone are symmetric. Some dynamical characteristics of these attractors are illustrated.

Automated summary

This article investigates a five-dimensional hyperchaotic system with five cross-product nonlinearities, identifying three different types of hyperchaotic and chaotic behaviors and the corresponding attractors. The fundamental dynamics, such as the onset of hyperchaos and chaos, routes to chaos, and coexistence of attractors, are analyzed theoretically and numerically. It is highlighted that the coexisting attractors in the 5D system are symmetrical.