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Evolution of quasiperiodicity in quorum-sensing coupled identical repressilators
Chaos. 2020. Vol. 30. No. 4. P. 043122-1–043122-9.
Stankevich N., Volkov E.
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.
Priority areas:
mathematics
Language:
English
Borovikova I., Okhrimenko G., Zamyatin V. et al., Journal of Structural Biology 2026 Vol. 218 No. 2 Article 108315
Single amino acid substitutions in the ATP-binding domain of ACVRL1, a key receptor in the bone morphogenetic protein (BMP) signaling pathway, are frequently classified as variants of uncertain significance (VUS), complicating molecular diagnosis for pulmonary arterial hypertension (PAH) and Hereditary Hemorrhagic Telangiectasia (HHT). Since aberrant ATP binding disrupts downstream SMAD1/5/8 phosphorylation, we employed molecular dynamics ...
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Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
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Background Cardiac fibrosis represents a significant health burden, with endothelial dysfunction and damaged
perivascular microenvironment increasingly recognized as key contributors to fibrotic remodeling. The urokinase
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Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
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Gonchenko S., Lerman L., Turaev D., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Yakuba V. I., Khutorskaya O. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
Added: May 15, 2026
Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
Added: May 15, 2026
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
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change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
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Added: May 14, 2026
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2026 Vol. 12 No. 1 P. 60–110
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Added: May 13, 2026
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Gerges M., Kosonogov V., OBM Neurobiology 2025 Vol. 9 No. 4 Article 310
Emotion regulation (ER) involves processes by which individuals modulate the intensity, duration, and expression of emotional responses, and its dysregulation is associated with a broad spectrum of psychological disorders. While traditionally conceptualized within psychological frameworks, ER is increasingly recognized as biologically grounded, involving intricate interactions between neurochemical, hormonal, and metabolic systems. This narrative review aims ...
Added: May 12, 2026
М.: ООО «Макс Пресс», 2026.
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Added: May 11, 2026
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We consider a plane wave, a radiation solution, and the sum of these solutions (total solution) for
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Added: May 11, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Shchur L., Antonov D., Burovski E., International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2026 P. 1–9
We present a simple model that simulates the possible influence of one society on another. Specifically, two societies evolve deterministically according to the well-known Nowak-May spatial game with the addition of mutual influence through connections that reflect the current states of the societies. This may be related to the influence of a global information resource ...
Added: April 20, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
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Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
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Kolesnikov A., / Series arXiv "math". 2025.
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Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
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Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
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