Multistability Route in a PWL Multi-scroll System through Fractional-Order Derivatives

Abstract Recently, it was discovered that the use of fractional derivatives induces the occurrence of multistable states in PWL systems with multiple scrolls. In this paper, we show the path of the system from monostable to multistable behavior by reducing the integration order. Using bifurcation diagrams, which describe the evolution of the attractor under the modification of the bifurcation parameter, and basins of attraction, we show that the system has a path to multistability, revealing the mechanism for the emergence of the behavior. The resulting dynamics shows the coexistence of up to n + 2 attractors, where n is the number of scrolls generated by the integer-order system. Moreover, the existence and uniqueness of the dynamics is proved by Poincar´e sections showing that the behaviors exist and coexist and are not a section of the same solution.