Mean Lyapunov exponent approach for the helicoidal Peyrard–Bishop model

In this Letter, the ordered and disordered regions of the field variable of an oscillator chain are studied. For this purpose, the mean Lyapunov exponent (MLE) theory is applied to the helicoidal Peyrard–Bishop (hPB) model. Applying mean Lyapunov exponent theory introduced by Shibata [H. Shibata, Physica A 264 (1999) 226] on the model shows that, the system is very sensitive to the potential parameters. By analyzing the behavior of the MLE with respect to the harmonic helicoidal coupling (K), it can be found that, it is not possible to set the Morse potential parameters of the hPB model in good qualitative agreement with other experimental and theoretical studies. Furthermore, the results show that the MLE is independent of length of the DNA chain. This achievement is important since it can be used to overcome the computational difficulties.

► The helicoidal Peyrard–Bishop model through Mean Lyapunov exponent (MLE) is investigated. ► It is shown that the system is very sensitive to the potential parameters. ► The MLE is independent of length of the DNA chain. ► The variation of the MLE with respect to the helicoidal coupling is discussed in detail.