Self-organizing dynamics

Since my Ph.D., I have devoted part of my research efforts to the problem of pattern formation for reaction-diffusion models based on networked systems.


  • With D. Fanelli and T. Carletti, I have shown that spatial patterns can spontaneously develop due to the unique topological organization (directed [1], multi-layered [2], Cartesian [3], anisotropic [4], and multigraph [5] of biological/ecological complex networks.

  • I have developed a new class of instabilities, termed topology driven, for reaction-diffusion models on directed networks [1]. It can be rigorously proven that a directed network (e.g., brain network) can firmly relax the Turing conditions for the formation of patterns.

  • We have also studied the effect that time delays have on the pattern formation process [6, 7]. In particular, proving the possibility of pattern forming in a single species system.

  • Also, with D. Fanelli, I have studied the emergence of macroscopic self-organization patterns that develop via a resonant amplification of the stochastic noise, which stems from finite-size fluctuations [8, 9, 10].

  • With P.K. Maini, I have explored the role of asymmetric diffusion in multicellular tissues in solving the Turing paradox and establishing asymmetric diffusion of morphogens, periodic boundary conditions, and the size of the multicellular system as key factors [11].

  • During B. A. Siebert's Ph.D. thesis, we proved that neuronal networks’ modularity shapes patterns of brain activity [11]. With J.P. Gleeson and A. Arenas, we have used a symmetry-breaking mechanism to explain the emergence of the chimera states [12].

References

[1] M. A., J.D. Challenger, F.S. Pavone, L. Sacconi, D. Fanelli, “The theory of pattern formation on directed networks”, Nature Communications, (IF: 14.919), 5, 4517 (2014)

[2] M. A., D.M. Busiello, T. Carletti, D. Fanelli, G. Planchon, “Turing patterns in multiplex networks”, Physical Review E (IF: 2.529), 90, 042814 (2014)

[3] M. A., D.M. Busiello, T. Carletti, D. Fanelli, G. Planchon, “Turing instabilities on Cartesian product networks”, Scientific Reports (IF: 4.525), 5, 12927 (2015)

[4] D.M. Busiello, G. Planchon, M. A., T. Carletti, D. Fanelli, “Pattern formation for reactive species undergoing anisotropic diffusion”, The European Physical Journal B (IF: 1.500), 88, 222 (2015)

[5] M. A., T. Carletti, D. Fanelli, “Tune the topology to create or destroy patterns”, The European Physical Journal B (IF: 1.500), 89, 260 (2016)

[6] J. Petit, M. A., D. Fanelli, B. Lauwens, T. Carletti, “Pattern formation in a two-component reaction-diffusion system with delayed processes on a network”, Physica A: Statistical Mechanics and its Applications (IF: 3.263), 462, 230 (2016)

[7] J. Petit, T. Carletti, M. A., D. Fanelli, “Delay-induced Turing-like waves for one-species reaction-diffusion model on a network”, EPL (Europhysics Letters) (IF: 2.753), 111, 58002 (2015)

[8] L. Cantini, C. Cianci, D. Fanelli, E. Masi, L. Barletti, M. A., “Stochastic amplification of spatial modes in a system with one diffusing species”, Journal of Mathematical Biology (IF: 2.259), 69, 1585-1608 (2013)

[9] M. A., T. Biancalani, D. Fanelli, A.J. McKane, “The linear noise approximation for reaction-diffusion systems on networks”, The European Physical Journal B (IF: 1.500), 86, 476 (2013)

[10] M. A., F. Di Patti, D. Fanelli, “Stochastic patterns on a network”, Physical Review E (IF: 2.529), 86, 046105 (2012)

[11] B. Siebert, C. L. Hall, J. P. Gleeson, M. A., “Role of modularity in self-organization dynamics in biological networks”, Physical Review E (IF: 2.529) 102 052306 (2020)

[12] M. A., B. A. Siebert, A. Arenas, J. P. Gleeson, “Symmetry-breaking mechanism for the formation of cluster chimera patterns", Chaos (IF: 3.642) 32, 013107 (2022)