A general stability criterion for multidimensional fractional-order network systems based on whole oscillation principle for small fractional-order operators

Abstract The research on the fractional-order network system (FONS, The derivative model of network system is fractional-order) has seen fruitful achievements, but ignores whether the fractional-order operator (The order of fractional derivatives α) in the FONS will affect its stability and dynamic characteristics. To tackle this problem, this paper adopts a new method to study the effect of fractional-operators in gamma functions on the dynamic state of the gamma function. This new method helps us to derive a novel dynamic principle of multidimensional FONS. We define it as the Whole Oscillation Principle. According to this principle, the choice of fractional operator reflects the dynamic oscillation characteristic of the multidimensional FONS in two dimensions of time and system state, thus better optimizing the complex case of the fractional-order system research process in the future. Furthermore, based on the auxiliary function-based integral inequality, the paper derives a new stability criterion for all dimensional FONS in the general form. Finally, the validity and correctness of the above theories are verified through numerical simulation to its good effect.