Stability and Bifurcation Analysis of a Discrete Fractional-Order SIR Rumor Propagation Model

Due to the long-memory effects inherent in fractional-order operators, the bifurcation analysis of fractional-order models is considerably more complicated than integer-order systems. Based on stability and bifurcation theories, this paper investigates the stability and bifurcation behavior of equilibrium points in a discrete fractional-order rumor propagation model using the complex frequency-domain method, which differs from the conventional approaches employed for discrete integer-order models. The directions and stability of periodic solutions arising from Neimark–Sacker bifurcations are further analyzed via the normal form method. Finally, two numerical examples are presented to illustrate the effectiveness of the theoretical results.