Nonlinear Sciences – Pattern Formation and Solitons
Scientific paper
2004-05-14
Nonlinear Sciences
Pattern Formation and Solitons
Scientific paper
10.1103/PhysRevE.70.026213
We study energy localization on the oscillator-chain proposed by Peyrard and Bishop to model the DNA. We search numerically for conditions with initial energy in a small subgroup of consecutive oscillators of a finite chain and such that the oscillation amplitude is small outside this subgroup for a long timescale. We use a localization criterion based on the information entropy and we verify numerically that such localized excitations exist when the nonlinear dynamics of the subgroup oscillates with a frequency inside the reactive band of the linear chain. We predict a mimium value for the Morse parameter $(\mu >2.25)$ (the only parameter of our normalized model), in agreement with the numerical calculations (an estimate for the biological value is $\mu =6.3$). For supercritical masses, we use canonical perturbation theory to expand the frequencies of the subgroup and we calculate an energy threshold in agreement with the numerical calculations.
Filho Elso Drigo
Luca Jayme de
Ponno Antonio
Ruggiero Jose Roberto
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