Complicated basins and the phenomenon of amplitude death in coupled hidden attractors

• Coexisting periodic and chaotic hidden attractors are observed.
• Riddled-like complicated basins of coexisting hidden attractors are observed.
• A new route to amplitude death is observed in time-delay coupled hidden attractors.

Understanding hidden attractors, whose basins of attraction do not contain the neighborhood of equilibrium of the system, are important in many physical applications. We observe riddled-like complicated basins of coexisting hidden attractors both in coupled and uncoupled systems. Amplitude death is observed in coupled hidden attractors with no fixed point using nonlinear interaction. A new route to amplitude death is observed in time-delay coupled hidden attractors. Numerical results are presented for systems with no or one stable fixed point. The applications are highlighted.