Dynamical effects of hypergraph links in a network of fractional-order complex systems

In recent times, the fractional-order dynamical networks have gained lots of interest across various scientific communities because it admits some important properties like infinite memory, genetic characteristics, and more degrees of freedom than an integer-order system. Because of these potential applications, the study of the collective behaviors of fractional-order complex networks has been investigated in the literature. In this work, we investigate the influence of higher-order interactions in fractional-order complex systems. We consider both two-body and three-body diffusive interactions. To elucidate the role of higher-order interaction, we show how the network of oscillators is synchronized for different values of fractional-order. The stability of synchronization is studied with a master stability function analysis. Our results show that higher-order interactions among complex networks help the earlier synchronization of networks with a lesser value of first-order coupling strengths in fractional-order complex simplices. Besides that, the fractional-order also shows a notable impact on synchronization of complex simplices. For the lower value of fractional-order, the systems get synchronized earlier, with lesser coupling strengths in both two-body and three-body interactions. To show the generality in the outcome, two neuron models, namely, Hindmarsh–Rose and Morris–Leccar, and a nonlinear Rössler oscillator are considered for our analysis.