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Gninzanlong CL, Ndjomatchoua FT, Tchawoua C. Taming intrinsic localized modes in a DNA lattice with damping, external force, and inhomogeneity. Phys Rev E 2019; 99:052210. [PMID: 31212565 DOI: 10.1103/physreve.99.052210] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2018] [Indexed: 11/07/2022]
Abstract
The dynamics of DNA in the presence of uniform damping and periodic force is studied. The damped and driven Joyeux-Buyukdagli model is used to investigate the formation of intrinsic localized modes (ILMs). Branches of ILMs are identified as well as their orbital stabilities. A study of the effect of inhomogeneity introduced into the DNA lattice and its ability to control chaotic behavior is conducted. It is seen that a single defect in the chain can induce synchronized spatiotemporal patterns, despite the fact that the entire set of oscillators and the impurity are chaotic when uncoupled. It is also shown that the periodic excitation applied on a specific site can drive the whole lattice into chaotic or regular spatial and temporal patterns.
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Affiliation(s)
| | - Frank Thomas Ndjomatchoua
- Sustainable Impact Platform, Adaptive Agronomy and Pest Ecology Cluster, International Rice Research Institute (IRRI), DAPO Box 7777-1301, Metro Manila, Philippines
| | - Clément Tchawoua
- Department of Physics, Faculty of Science, University of Yaoundé 1, P.O. Box 812, Yaoundé, Cameroon
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Mulhern C, Bialonski S, Kantz H. Extreme events due to localization of energy. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:012918. [PMID: 25679693 DOI: 10.1103/physreve.91.012918] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2014] [Indexed: 06/04/2023]
Abstract
We study a one-dimensional chain of harmonically coupled units in an asymmetric anharmonic soft potential. Due to nonlinear localization of energy, this system exhibits extreme events in the sense that individual elements of the chain show very large excitations. A detailed statistical analysis of extremes in this system reveals some unexpected properties, e.g., a pronounced pattern in the interevent interval statistics. We relate these statistical properties to underlying system dynamics and notice that often when extreme events occur the system dynamics adopts (at least locally) an oscillatory behavior, resulting in, for example, a quick succession of such events. The model therefore might serve as a paradigmatic model for the study of the interplay of nonlinearity, energy transport, and extreme events.
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Affiliation(s)
- Colm Mulhern
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany
| | - Stephan Bialonski
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany
| | - Holger Kantz
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Str. 38, D-01187 Dresden, Germany
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TABI CONRADBERTRAND, MOHAMADOU ALIDOU, KOFANE TIMOLEONCREPIN. LOCALIZED BREATHER-LIKE EXCITATIONS IN THE HELICOIDAL PEYRARD–BISHOP MODEL OF DNA. INT J BIOMATH 2011. [DOI: 10.1142/s1793524509000777] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We consider the one-dimensional helicoidal Peyrard–Bishop (PB) model of DNA dynamics. By means of a method based on the Jacobian elliptic functions, we obtain the exact analytical solution which describes the modulational instability and the propagation of a bright solitary wave on a continuous wave background. It is shown that these solutions depend on the modulational (or Benjamin-Feir) instability criterion. Numerical simulations of their propagation show these excitations to be long-lived and suggest that they are physically relevant for DNA.
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Affiliation(s)
- CONRAD BERTRAND TABI
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P. O. Box 812, Yaounde, Cameroon
- The Abdus Salam, International Center for Theoretical Physics, P. O. Box 586, Strada Costiera 11, I-34014 Trieste, Italy
| | - ALIDOU MOHAMADOU
- Condensed Matter Laboratory, Department of Physics, Faculty of Science, University of Douala, P. O. Box 24157, Douala, Cameroon
| | - TIMOLEON CREPIN KOFANE
- Laboratory of Mechanics, Department of Physics, Faculty of Science, University of Yaounde I, P. O. Box 812, Yaounde, Cameroon
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English LQ, Palmero F, Sievers AJ, Kevrekidis PG, Barnak DH. Traveling and stationary intrinsic localized modes and their spatial control in electrical lattices. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:046605. [PMID: 20481851 DOI: 10.1103/physreve.81.046605] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/12/2010] [Indexed: 05/29/2023]
Abstract
This work focuses on the production of both stationary and traveling intrinsic localized modes (ILMs), also known as discrete breathers, in two closely related electrical lattices; we demonstrate experimentally that the interplay between these two ILM types can be utilized for the purpose of spatial control. We describe a novel mechanism that is responsible for the motion of driven ILMs in this system, and quantify this effect by modeling in some detail the electrical components comprising the lattice.
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Affiliation(s)
- L Q English
- Deptartment of Physics and Astronomy, Dickinson College, Carlisle, Pennsylvania 17013, USA
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Palmero F, Carretero-González R, Cuevas J, Kevrekidis PG, Królikowski W. Solitons in one-dimensional nonlinear Schrödinger lattices with a local inhomogeneity. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:036614. [PMID: 18517550 DOI: 10.1103/physreve.77.036614] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/13/2007] [Indexed: 05/26/2023]
Abstract
In this paper we analyze the existence, stability, dynamical formation, and mobility properties of localized solutions in a one-dimensional system described by the discrete nonlinear Schrödinger equation with a linear point defect. We consider both attractive and repulsive defects in a focusing lattice. Among our main findings are (a) the destabilization of the on-site mode centered at the defect in the repulsive case, (b) the disappearance of localized modes in the vicinity of the defect due to saddle-node bifurcations for sufficiently strong defects of either type, (c) the decrease of the amplitude formation threshold for attractive and its increase for repulsive defects, and (d) the detailed elucidation as a function of initial speed and defect strength of the different regimes (trapping, trapping and reflection, pure reflection, and pure transmission) of interaction of a moving localized mode with the defect.
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Affiliation(s)
- F Palmero
- Nonlinear Dynamical Systems Group, Computational Science Research Center and Department of Mathematics and Statistics, San Diego State University, San Diego, CA 92182-7720, USA.
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Zamora-Sillero E, Shapovalov AV, Esteban FJ. Formation, control, and dynamics of N localized structures in the Peyrard-Bishop model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:066603. [PMID: 18233933 DOI: 10.1103/physreve.76.066603] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2007] [Indexed: 05/25/2023]
Abstract
We explore in detail the creation of stable localized structures in the form of localized energy distributions that arise from general initial conditions in the Peyrard-Bishop (PB) model. By means of a method based on the inverse scattering transform we study the solutions of PB model equations obtained in the form of planar waves whose amplitudes are described by the nonlinear Schrödinger equation (NLS). For localized initial conditions different from the pure N-soliton shape, we have obtained analytical results that predict and control the number, amplitude, and velocity of the NLS solitary waves. To verify the validity of these results we have carried out numerical simulations of the PB model with the use of realistic values of parameters and the initial conditions in the form of planar waves whose modulated amplitudes are given by the examples studied in the NLS. In the simulations we have found that N localized structures arise in agreement with the prediction of the analytical results obtained in the NLS.
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Affiliation(s)
- Elías Zamora-Sillero
- Departamento de Fisica Aplicada I, E.U.P. Universidad de Sevilla Virgen de Africa 7, 41011 Sevilla, Spain.
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Larsen PV, Christiansen PL, Bang O, Archilla JFR, Gaididei YB. Bubble generation in a twisted and bent DNA-like model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:036609. [PMID: 15524658 DOI: 10.1103/physreve.70.036609] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/15/2004] [Revised: 06/14/2004] [Indexed: 05/24/2023]
Abstract
The DNA molecule is modeled by a parabola embedded chain with long-range interactions between twisted base pair dipoles. A mechanism for bubble generation is presented and investigated in two different configurations. Using random normally distributed initial conditions to simulate thermal fluctuations, a relationship between bubble generation, twist and curvature is established. An analytical approach supports the numerical results.
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Affiliation(s)
- P V Larsen
- Informatics and Mathematical Modelling and Department of Mathematics, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
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Cuevas J, Kevrekidis PG. Breather statics and dynamics in Klein-Gordon chains with a bend. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:056609. [PMID: 15244965 DOI: 10.1103/physreve.69.056609] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/30/2003] [Indexed: 05/24/2023]
Abstract
In this paper, we examine a nonlinear model with an impurity emulating a bend. We justify the geometric interpretation of the model and connect it with earlier work on models including geometric effects. We focus on both the bifurcation and stability analysis of the modes that emerge as a function of the strength of the bend angle, but we also examine dynamical effects including the scattering of mobile localized modes (discrete breathers) off of such a geometric structure. The potential outcomes of such numerical experiments (including transmission, trapping within the bend as well as reflection) are highlighted and qualitatively explained. Such models are of interest both theoretically in understanding the interplay of breathers with curvature, but also practically in simple models of photonic crystals or of bent chains of DNA.
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Affiliation(s)
- J Cuevas
- Grupo de Física No Lineal, Departamento de Física Aplicada I, ETSI Informática, Universidad de Sevilla, Avenida Reina Mercedes, s/n, 41012-Seville, Spain.
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Larsen PV, Christiansen PL, Bang O, Archilla JFR, Gaididei YB. Energy funneling in a bent chain of Morse oscillators with long-range coupling. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 69:026603. [PMID: 14995576 DOI: 10.1103/physreve.69.026603] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2003] [Indexed: 05/24/2023]
Abstract
A bent chain of coupled Morse oscillators with long-range dispersive interaction is considered. Moving localized excitations may be trapped in the bending region. Thus chain geometry acts like an impurity. An energy funneling effect is observed in the case of random initial conditions.
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Affiliation(s)
- P V Larsen
- Informatics and Mathematical Modelling, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark.
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Miroshnichenko AE, Flach S, Malomed B. Resonant scattering of solitons. CHAOS (WOODBURY, N.Y.) 2003; 13:874-879. [PMID: 12946179 DOI: 10.1063/1.1597071] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We study the scattering of solitons in the nonlinear Schrödinger equation on local inhomogeneities which may give rise to resonant transmission and reflection. In both cases, we derive resonance conditions for the soliton's velocity. The analytical predictions are tested numerically in regimes characterized by various time scales. Special attention is paid to intermode interactions and their effect on coherence, decoherence, and dephasing of plane-wave modes which build up the soliton.
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Affiliation(s)
- A E Miroshnichenko
- Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzer Strasse 38, D-01187 Dresden, Germany
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Kevrekidis PG, Kivshar YS, Kovalev AS. Instabilities and bifurcations of nonlinear impurity modes. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 67:046604. [PMID: 12786506 DOI: 10.1103/physreve.67.046604] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/16/2002] [Indexed: 05/24/2023]
Abstract
We study the structure and stability of nonlinear impurity modes in the discrete nonlinear Schrödinger equation with a single on-site nonlinear impurity emphasizing the effects of interplay between discreteness, nonlinearity, and disorder. We show how the interaction of a nonlinear localized mode (a discrete soliton or discrete breather) with a repulsive impurity generates a family of stationary states near the impurity site, as well as examine both theoretical and numerical criteria for the transition between different localized states via a cascade of bifurcations.
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Affiliation(s)
- Panayotis G Kevrekidis
- Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts 01003-4515, USA
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