Chaos break and synchrony enrichment within Hindmarsh–Rose-type memristive neural models

Nonlinear Dynamics - The fluctuation of ions concentration across the cell membrane of neuron can generate a time varying electromagnetic field. Thus, memristors are used to realize the coupling...     

Long-range interactions and wave patterns in a DNA model

The three-dimensional structures of elastin-like polypeptides Val1-Pro2-Gly3-Xaa4-Gly5 were investigated by using the multicanonical Monte Carlo (MC) simulation procedure. By substituting different amino acids in the fourth position of the sequence, the thermodynamical variables are calculated in vacuo and in solvent to determine the hydrophobicity dependence of the conformational transition temperatures of the peptides. Resultant hydrophobicity scale is in good agreement with many hydrophobicity scales.     

Modulated Wave Packets in DNA and Impact of Viscosity

We study the nonlinear dynamics of a DNA molecular system at physiological temperature in a viscous media by using the Peyrard-Bishop model. The nonlinear dynamics of the above system is shown to be governed by the discrete complex Cinzburg-Landau equation. In the non-viscous limit, the equation reduces to the nonlinear Schroedinger equation. Modulational instability criteria are derived for both the cases. On the basis of these criteria, numerical simulations are made, which confirm the analytical predictions. The planar wave solution used as the initial condition makes localized oscillations of base pairs and causes energy localization. The results also show that the viscosity of the solvent in the surrounding damps out the amplitude of wave patterns.     

Modulational instability in the anharmonic Peyrard-Bishop model of DNA

We report on the presence of modulational instability and the generation of soliton-like excitations in DNA nucleotides. Taking the Peyrard-Bishop-Dauxois model of DNA dynamics as an example, we show that the original difference equation for the DNA dynamics can be reduced to the Salerno equation. We derive the MI criterion in this case. The effect of the anharmonic stacking term on the domain of instability/stability is pointed out. Numerical simulations show the validity of the analytical approach with the generation of wave packets provided that the wave numbers fall in the instability domain. The impact of the anharmonic stacking interactions is investigated and these are found to give rise to a spectrum of behaviours which corroborates experimental facts.     

Hopf bifurcations on invariant manifolds of a modified Fitzhugh–Nagumo model

Nonlinear Dynamics - In this paper, we investigate the nonlinear vibration of a metamaterial structure that consists of a rotating cantilever beam attached to a periodic array of...     

Wave propagation of nonlinear modes and formation of bubble in a two-component helicoidal lattice

Through the multiplescale expansion, we show that the dynamics of modulated waves in atwo-component helicoidal one-dimensional model is governed by thenonlinear Schrödinger (NLS) equation. We study the occurrence ofpatterns formation in such a system. The impact of the helicoidalcoupling is also studied which reveals that high values of thehelicoidal coupling constant contribute to regulate information andcharge transport throughout the two-chain model. This is madepossible due to the superposition of optical and acoustic modes. Inaddition, the model is used to investigate internal dynamics of DNA.It is shown that the opening of the double helix of the DNA itselfis controlled by the resonance mode, where the unzipping of thedouble helix has been illustrated by numerical simulations.Furthermore, the shape of the eyelike shape previously observed inexperiments of thermal denaturation of DNA is numerically obtained.     

Modulational instability and exact soliton solutions for a twist-opening model of DNA dynamics

We study the nonlinear dynamics of DNA which takes into account the twist-opening interactions due to the helicoidal molecular geometry. The small amplitude dynamics of the model is shown to be governed by a solution of a set of coupled nonlinear Schrödinger equations. We analyze the modulational instability and solitary wave solution in the case. On the basis of this system, we present the condition for modulation instability occurrence and attention is paid to the impact of the backbone elastic constant K. It is shown that high values of K extend the instability region. Through the Jacobian elliptic function method, we derive a set of exact solutions of the twist-opening model of DNA. These solutions include, Jacobian periodic solution as well as kink and kink-bubble solitons.     

Discrete charge patterns in a Holstein‐SSH DNA lattice

DNA nonlinear charge transport is addressed in a combined Holstein–Su–Schrieffer–Heeger (HSSH) model. In the adiabatic approximation the dynamics of the system is shown to be governed by a modified discrete nonlinear Schrödinger (MDNLS) equation, where charge‐lattice coupling parameters are obvious. Attention is paid to the effective coupling parameter, , between charge and internal molecular vibrations, which importantly influences the stability/instability features of the plane wave, solution to the MDNLS equation. Region of instability are remarkably reduced, therefore predicting that increasing could progressively quench charge transport. This is confirmed by numerical simulations on the generic HSSH model, where only the charge density is excited and drives the dynamics of the global system. Polarons, as well as longitudinal and transversal nonlinear waves, are obtained and the dependence of charge transport on DNA conformation is discussed. Accordingly, the longtime evolution of the found polarons is studied and we observe a progressive extinction of its temporal evolution as increases. © 2014 Wiley Periodicals, Inc.     

Intramolecular vibrations and noise effects on pattern formation in a molecular helix

Modulational instability in a biexciton molecular chain is addressed. We show that the model can be reduced to a set of three coupled equations: two nonlinear Schr?dinger equations and a Boussinesq equation. The linear stability analysis of continuous wave solutions of the coupled systems is performed and the growth rate of instability is found numerically. Simulations of the full discrete systems reveal some behaviors of modulational instability, since wave patterns are observed for the excitons and the phonon spectrum. We also take the effect of thermal fluctuations into account and we numerically study both the stability and the instability of the plane waves under 300 K. The plane wave is found to be stable under modulation, but displays a gradual increase of the wave amplitudes. Under modulation, the same behaviors are observed and wave patterns are found to resist thermal fluctuations, which is in agreement with earlier research on localized structure stability under thermal noise.