Super extreme multistability in a two-dimensional fractional-order forced neural model

This paper investigates the dynamics of a memristive single-neuron model by considering the fractional-order derivatives. The bifurcation diagrams are obtained according to the fractional order and the systems’ parameters. It is shown that the system's dynamics can vary considerably by changing the fractional order, depending on the systems’ parameters. Furthermore, the results represent the emergence of multiple coexisting attractors by decreasing the derivative order from the integer one. For some fractional orders, infinite attractors coexist, leading to extreme multistability. Moreover, extreme multistability is observed by changing both of the initial conditions to which we refer super extreme multistability. To the best of our knowledge, this is the first observation of extreme multistability in 2D dynamical systems, which occurs due to fractional order.