Mean Lyapunov exponent approach for the helicoidal Peyrard–Bishop model

On The Features Solitary Wave Solutions for the DoubleStructures Model of DNA

“…Since the structure of DNA double helix has been discovered by Watson and Crick in 1953 [2]. Many researchers, especially ones in theoretical physics and nonlinear dynamics and also triggered the formulation of several simple models of nonlinear DNA dynamics corresponding to geometric structure, namely, the DNA double-stranded [3][4][5][6][7][8][9][10][11][12][13][14] or the double helix [15][16][17][18][19][20][21][22][23][24][25][26][27][28]. These models had been developed during the past decade to describe the nonlinear dynamics properties of open base-pairs in DNA, which commonly called denaturation bubbles [29].…”

Comment on “Modeling the electrical conduction in DNA nanowires: Charge transfer and lattice fluctuation theories”

“…Conversely, the spatial patterns are more ordered when the values of the mean Lyapunov exponent are smaller. Previously this method has been applied to some DNA models and there has been some success in parameter selection rules for Peyrard-Bishop models [4,5].In the case of MLE behavior with respect to the temperature, Behnia and Fathizadeh [6] coupled the system to a thermal bath and determined MLE as a function of temperature; this is shown in Fig. 5 of the paper.…”

“…Conversely, the spatial patterns are more ordered when the values of the mean Lyapunov exponent are smaller. Previously this method has been applied to some DNA models and there has been some success in parameter selection rules for Peyrard-Bishop models [4,5].…”