The dynamics of three three-dimensional repressilators globally coupled by a quorum sensing mechanism was numerically studied. This number (three) of coupled repressilators is sufficient to obtain such a set of self-consistent oscillation frequencies of signal molecules in the mean field that results in the appearance of self-organized quasiperiodicity and its complex evolution over wide areas of model parameters. Numerically analyzing the invariant curves as a function of coupling strength, we observed torus doubling, three torus arising via quasiperiodic Hopf bifurcation, the emergence of resonant cycles, and secondary Neimark–Sacker bifurcation. A gradual increase in the oscillation amplitude leads to chaotizations of the tori and to the birth of weak, but multidimensional chaos.
Evolution of quasiperiodicity in quorum-sensing coupled identical repressilators
Also at: Department of Radio-Electronics and Telecommunications, Yuri Gagarin State Technical University of Saratov, 77 Politekhnicheskaya str., Saratov 410054, Russia and Department of Applied Cybernetics, St. Petersburg State University, Saint-Petersburg, Peterhof, 28 Universitetskiy proezd, St. Petersburg 198504, Russia.
N. Stankevich, E. Volkov; Evolution of quasiperiodicity in quorum-sensing coupled identical repressilators. Chaos 1 April 2020; 30 (4): 043122. https://doi.org/10.1063/1.5140696
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