Extreme Multistability in a Dynamic System with Infinitely Many 2D Hidden Attractors

Extreme multistability can be understood as a dynamical behavior in which new attractors arise from infinitesimal variations in initial conditions. In this chapter, we introduce a novel continuous-time dynamical system governed by periodic signals as the main nonlinearities that converges to 2D infinitely many chaotic attractors in the phase space. Notably, the chaotic system has no stationary equilibrium points. In addition, a single parameter controls the class of a hidden attractor, that is, from an infinite mesh of equilibria to no equilibrium points. Theoretical and numerical experiments, including equilibrium point analysis and Poincaré maps, reveal the striking properties of the chaotic system. The resulting outcomes open up possibilities for application in chaos-based data encryption.