Stability Analysis of a Fractional-Order Model for Abstinence Behavior of Registration on the Electoral Lists

Abstract

In this work, we propose a fractional-order model that describes the dynamics of citizens who have the right to register on the electoral lists and the negative influence of abstainers on the potential electors. By using Routh–Hurwitz criteria and constructing Lyapunov functions, the local and the global stability of abstaining-free equilibrium and abstaining equilibrium are obtained. Finally, some numerical simulations are performed to verify the theoretical analysis, and they are given for different parameter setting of the order of derivative $\alpha$.