Here we propose that viruses emerging in the human population undergo an evolution that is conditioned by the rules of chaos. Our data support the notion that the initial growth rate "r" affects the chances of the virus to establish a long-lasting relationship with the new host. Indeed, an emerging virus is able to spread and adapt only when it displays an initial r falling in a range frankly associated with chaotic growth.
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http://www.ncbi.nlm.nih.gov/pmc/articles/PMC10449193 | PMC |
http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0290453 | PLOS |
Chaos
January 2025
Institute for Theoretical Physics, University of Leipzig, D-04081 Leipzig, Germany.
We consider a dynamical system undergoing a saddle-node bifurcation with an explicitly time-dependent parameter p(t). The combined dynamics can be considered a dynamical system where p is a slowly evolving parameter. Here, we investigate settings where the parameter features an overshoot.
View Article and Find Full Text PDFChaos
January 2025
Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526, USA.
This paper focuses on distinguishing classes of dynamical behavior for one- and two-dimensional torus maps, in particular, between orbits that are incommensurate, resonant, periodic, or chaotic. We first consider Arnold's circle map, for which there is a universal power law for the fraction of nonresonant orbits as a function of the amplitude of the nonlinearity. Our methods give a more precise calculation of the coefficients for this power law.
View Article and Find Full Text PDFChaos
January 2025
Instituto de Física, Universidad Nacional Autónoma de México, Mexico City 04510, Mexico.
We study an exactly solvable random walk model with long-range memory on arbitrary networks. The walker performs unbiased random steps to nearest-neighbor nodes and intermittently resets to previously visited nodes in a preferential way such that the most visited nodes have proportionally a higher probability to be chosen for revisit. The occupation probability can be expressed as a sum over the eigenmodes of the standard random walk matrix of the network, where the amplitudes slowly decay as power-laws at large times, instead of exponentially.
View Article and Find Full Text PDFEntropy (Basel)
December 2024
Istituto Nazionale di Alta Matematica (INdAM), 00185 Rome, Italy.
The status of the Second Law of Thermodynamics, even in the 21st century, is not as certain as when Arthur Eddington wrote about it a hundred years ago. It is not only about the truth of this law, but rather about its strict and exhaustive formulation. In the previous article, it was shown that two of the three most famous thermodynamic formulations of the Second Law of Thermodynamics are non-exhaustive.
View Article and Find Full Text PDFBifurcations are one of the most remarkable features of dynamical systems. Corral et al. [Sci.
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