Extreme Multistability in Simple Area-Preserving Map

Initial condition-relied extreme multistability has been recently found in many continuous dynamical systems. However, such a specific phenomenon has not yet been discovered in a discrete iterative map. To investigate this phenomenon, this paper proposes a two-dimensional conservative map only with one sine nonlinearity. The proposed simple discrete map is area-preserving in the phase space and displays the coexistence of infinite chaotic and quasi-periodic orbits caused by infinite fixed points. Multiple numerical results indicate that the area-preserving chaotic and quasi-periodic orbits have the initial condition-relied quasi-periodic route to chaos and initial condition-boosting bifurcation dynamics, which allow the simple area-preserving map to emerge the complex phenomenon of extreme multistability. Furthermore, a microcontroller-based hardware platform is developed to implement the initial condition-boosting chaotic signals.