Fractional cyber-neural systems -- a brief survey

Reed, Emily; Chatterjee, Sarthak; Ramos, Guilherme; Bogdan, Paul; Pequito, Sérgio

doi:10.48550/arxiv.2112.08535

Cited by 1 publication

(1 citation statement)

References 120 publications

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“…Fractional-order calculus and fractional-order dynamical networks provide efficient and compact mathematical tools for representing long-term memory with power-law memory dependencies [18][19][20][21][22][23][24][25][26][27][28][29] . These dependencies are captured by using a fractional-order derivative denoted by � α , which is the so-called Grünwald-Letnikov discretization of the fractional derivative, where α = (α 1 , α 2 , .…”

Section: Methodsmentioning

confidence: 99%

The role of long-term power-law memory in controlling large-scale dynamical networks

Reed,

Ramos,

Bogdan

et al. 2023

Sci Rep

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Controlling large-scale dynamical networks is crucial to understand and, ultimately, craft the evolution of complex behavior. While broadly speaking we understand how to control Markov dynamical networks, where the current state is only a function of its previous state, we lack a general understanding of how to control dynamical networks whose current state depends on states in the distant past (i.e. long-term memory). Therefore, we require a different way to analyze and control the more prevalent long-term memory dynamical networks. Herein, we propose a new approach to control dynamical networks exhibiting long-term power-law memory dependencies. Our newly proposed method enables us to find the minimum number of driven nodes (i.e. the state vertices in the network that are connected to one and only one input) and their placement to control a long-term power-law memory dynamical network given a specific time-horizon, which we define as the ‘time-to-control’. Remarkably, we provide evidence that long-term power-law memory dynamical networks require considerably fewer driven nodes to steer the network’s state to a desired goal for any given time-to-control as compared with Markov dynamical networks. Finally, our method can be used as a tool to determine the existence of long-term memory dynamics in networks.

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