2 research outputs found
Pattern formation and bifurcation analysis of delay induced fractional-order epidemic spreading on networks
The spontaneous emergence of ordered structures, known as Turing patterns, in
complex networks is a phenomenon that holds potential applications across
diverse scientific fields, including biology, chemistry, and physics. Here, we
present a novel delayed fractional-order
susceptible-infected-recovered-susceptible (SIRS) reaction-diffusion model
functioning on a network, which is typically used to simulate disease
transmission but can also model rumor propagation in social contexts. Our
theoretical analysis establishes the Turing instability resulting from delay,
and we support our conclusions through numerical experiments. We identify the
unique impacts of delay, average network degree, and diffusion rate on pattern
formation. The primary outcomes of our study are: (i) Delays cause system
instability, mainly evidenced by periodic temporal fluctuations; (ii) The
average network degree produces periodic oscillatory states in uneven spatial
distributions; (iii) The combined influence of diffusion rate and delay results
in irregular oscillations in both time and space. However, we also find that
fractional-order can suppress the formation of spatiotemporal patterns. These
findings are crucial for comprehending the impact of network structure on the
dynamics of fractional-order systems.Comment: 23 pages, 9 figure