We demonstrate that period-doubled discrete breathers appear from the anticontinuum limit of the driven Peyrard-Bishop-Dauxois model of DNA. These novel breathers result from a stability overlap between subharmonic solutions of the driven Morse oscillator. Subharmonic breathers exist whenever a stability overlap is present within the Feigenbaum cascade to chaos and therefore an entire cascade of such breathers exists. This phenomenon is present in any driven lattice where the on-site potential admits subharmonic solutions. In DNA these breathers may have ramifications for cellular gene expression.
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An introduction to the unpublished book "Reflections on a Tube" by Mitchell J. Feigenbaum.
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Département de Physique Théorique and Section de Mathématiques, University of Geneva, Geneva, Switzerland.
This paper is an adaptation of the introduction to a book project by the late Mitchell J. Feigenbaum (1944-2019). While Feigenbaum is certainly mostly known for his theory of period doubling cascades, he had a lifelong interest in optics.
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Biofisika Institutua (UPV/EHU, CSIC) and Fundación Biofísica Bizkaia, Leioa E-48940, Spain.
The emergence of collective oscillations and synchronization is a widespread phenomenon in complex systems. While widely studied in the setting of dynamical systems, this phenomenon is not well understood in the context of out-of-equilibrium phase transitions in many-body systems. Here we consider three classical lattice models, namely the Ising, the Blume-Capel, and the Potts models, provided with a feedback among the order and control parameters.
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International Research and Educational Centre for Physics of Nanostructures, ITMO University, Kronverksky Prospekt 49, Bldg. A, St. Petersburg 197101, Russia.
We have numerically investigated the dynamics of charged microparticles in a "five-wire" surface radio-frequency trap. The period-doubling bifurcation conditions have been shown to depend on the particle, the trap, and the alternating voltage parameters. For a comprehensive study of the dynamics chaotization through a cascade of period doubling, we have used Fourier analysis of a particle trajectory as well as the calculations of a non-trivial Lyapunov exponent map.
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Institute of Physics, Saratov State University, Astrakhanskaya str. 83, 410012 Saratov, Russia.
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