Synchronization in a Multiplex Network of Nonidentical Fractional-Order Neurons

Fractional-order neuronal models that include memory effects can describe the rich dynamics of the firing of the neurons. This paper studies synchronization problems in a multiple network of Caputo–Fabrizio type fractional order neurons in which the orders of the derivatives in the layers are different. It is observed that the intralayer synchronization state occurs in weaker intralayer couplings when using nonidentical fractional-order derivatives rather than integer-order or identical fractional orders. Furthermore, the needed interlayer coupling strength for interlayer near synchronization decreases for lower fractional orders. The dynamics of the neurons in nonidentical layers are also considered. It is shown that in lower fractional orders, the neurons’ dynamics change to periodic when the near synchronization state occurs. Moreover, decreasing the derivative order leads to incrementing the frequency of the bursts in the synchronization manifold, which is in contrast to the behavior of the single neuron.