Research on the Synchronization Control of Fractional-Order Complex Networks Based on Switching Topology

Abstract

Abstract: In the contemporary epoch, bolstered by information technology, the quintessence of networks is ubiquitously manifested, with a plethora of network types—ranging from the Internet, vehicular traffic frameworks, electrical distribution systems, cellular communication matrices, to social interconnection webs—being intricately woven into the fabric of societal functionality and quotidian existence. The domain of complex networks has burgeoned into a fervently pursued research vector, magnetizing an eclectic cohort of investigators from disciplines as variegated as mathematics, biosciences, and engineering. Notably, the fractional calculus has eclipsed its integer-order counterpart by offering enhanced precision in the depiction of real-world systems and phenomena. Consequently, the infusion of fractional calculus into the modeling of complex networks, to dissect their dynamic attributes and attendant control paradigms, has crystallized as a research nexus of burgeoning interest, eliciting scholarly discourse at both national and international echelons. [Purpose] This inquiry into the synchronization control of fractional-order complex networks, predicated on switching topology, endeavors to harness said topology as a scaffold for probing the synchronicity inherent within fractional-order complex networks. The objective is to augment the operational efficacy of these networks, broaden their sphere of applicability, and fortify the synchronal linkage amongst fractional-order complex networks and their counterparts. [Method] Predominantly, this exploration is underpinned by a synthesis of bibliographic scrutiny and analytical modeling, employing an extensive compendium of model equations to elucidate the subject matter. The spotlight is cast upon the Caputo fractional-order differential equation, with a focus on assaying the stability traits of its equilibrium junctures and formulating more expansive and pragmatic conditions for stability. In addition, to facilitate the precise estimation of elusive topologies within complex networks, a supplementary network—comprising isolated nodes and a regulatory protocol—is conceptualized. [Results] The findings suggest that the investigation into synchronization control based on switching topology propels the advancement of fractional-order complex networks and has substantial reference value. It serves to substantiate, to a certain degree, the postulations of antecedent theorists and chart a trajectory for ensuing scholarly endeavors in cognate domains, thereby perpetually amplifying the pragmatic utility of fractional-order complex networks.