Fractal-induced multistability in Chua’s circuit

We study the emergence of multistability in a Chua’s circuit induced by fractal Chua’s diode with piecewise-linear self-similar segments. It not only involves the latest reported matryoshka attractors, but generates additional heterogeneous ones. In the case considered, we observe the dynamical evolution from bistable states to coexisting heterogeneous and matryoshka multistable states. In specific, the fractal-induced emergence of coexisting one pair of matryoshka chaotic hollows, two pairs of chaotic branches, one periodic limit cycle, and five locally stable points is confirmed. For different scales of the initial conditions, the coexisting attractors with different amplitudes emerge or disappear, leaving the system mixed multistable. We further study the basins of attraction for investigating the multiscale self-similar structure in the regime of this mixed multistability. The observed multistability brings about a new source of unpredictability and complexity in a simple deterministic piecewise-linear system.