https://doi.org/10.1140/epjs/s11734-025-02007-x
Regular Article
Pattern formation in a rumor model under dispersion
1
School of Physics, University of Hyderabad, 500046, Gachibowli, Hyderabad, India
2
Department of Mathematics, School of Engineering, Dayananda Sagar University, 562112, Bengaluru, India
3
Institute of Science and Technology for Brain-Inspired Intelligence, Fudan University, 200433, Shanghai, China
4
Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924, Lodz, Poland
5
Center for Computational Natural Science and Bioinformatics, International Institute of Informational Technology, 500032, Gachibowli, Hyderabad, India
6
School of Engineering & Technology, BML Munjal University, 122413, Gurugram, Haryana, India
7
Center for Advanced Data and Computational Science, BML Munjal University, 122413, Gurugram, Haryana, India
8
Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, 700032, Kolkata, West Bengal, India
9
The biomedical research center (BMRC), International Institute of Information Technology, Hyderabad, 50032, India
a
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Received:
13
May
2025
Accepted:
1
October
2025
Published online:
15
November
2025
Abstract
Some instabilities often trigger pattern formation in reaction diffusion systems, offering valuable insights on the underlying dynamics and interactions driving the emergence of patterns in numerous animate and inanimate systems. We investigate formation of Turing patterns resulting in a generalized two-compartment (Innocent-Spreader) model for rumor spreading through spatial dispersion. Our analysis reveals the significance of diffusion on the evolution of holes from stripes and as well as the continuous growth of spots. Especially, we explore the role of some crucial parameters, including the rate of media correction, inhibition, forgetting, and self-correction on controlling the spreading of rumors. Finally, we check how initial conditions influence the emergence of mixed-mode patterns, characterized by a low diffusion rate.
N. Saha and Y. Li have equally contributed to this work.
© The Author(s) 2025
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