Taming intrinsic localized modes in a DNA lattice with damping, external force, and inhomogeneity

Gninzanlong, Carlos Lawrence; Ndjomatchoua, Frank T.; Tchawoua, Clément

doi:10.1103/physreve.99.052210

Cited by 13 publications

(2 citation statements)

References 64 publications

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“…(e) The case h > h e corresponds to the green curve of Fig. 3 and the corresponding solution is similar to that obtained by the integral (22).…”

Section: Introductionsupporting

confidence: 72%

Singular Nonlinear Equation Class : Theoretical and Experimental Concept

Nguetcho

2021

Preprint

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This work generalizes and extends our work in refs [10,29,37], dealing a theoretical model of a monoatomic chain immersed in a potential of periodic and deformable substrate, the third and fourth non-linearities being taken into account. Looking at the analytical localized modes provides an extended interpretation of system dynamics based upon modes existence and yields an extended form of the nonlinear Schrodinger equation to describe the eikonal wave's complex amplitude. In this equation, the coeffcients depend on the wavenumber, whereas the parallel with the nonlinear transmission electrical line introduced in references results in [1,2] not fully resolved dynamic equations. So far, only specific solutions have been presented. Our dynamic study thus presents a theoretical prediction for their experimental set up. In contrast to previous works done for particular values of the wavenumber, namely on the behavior of gap (k = 0 and k = π) solutions of the model [10], or for k (k = ±2π=3) in the central bandpass area [37], we consider here rather behaviors of the system when the angular frequency is arbitrary. By using bifurcation theory of planar dynamical systems and investigating the dynamical behavior, we derive a variety of solutions corresponding to the phase trajectories under different parameter conditions.

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“…(e) The case h > h e corresponds to the green curve of Fig. 3 and the corresponding solution is similar to that obtained by the integral (22).…”

Section: Introductionsupporting

confidence: 72%

Singular Nonlinear Equation Class : Theoretical and Experimental Concept

Nguetcho

2021

Preprint

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“…Generally, the occurrence of chaotic behaviors limits the performance of the model and may cause instability in engineering applications, wear and additional energy dissipation in solid-friction and insufficient output power in electronic applications, so it is of significance to control chaos in the system. [3][4][5][6][7] Chaos control has been studied for three decades since the pioneering work of Ott, Grebogi, and Yorke. [8] Later on, many control methods were proposed such as the feedback control method, [9][10][11][12][13] (non-)linear control method, [14][15][16] and adaptive control method.…”

Section: Introductionmentioning

confidence: 99%

Control of chaos in Frenkel–Kontorova model using reinforcement learning*

Lei

Han

2021

Chinese Phys. B

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It is shown that we can control spatiotemporal chaos in the Frenkel–Kontorova (FK) model by a model-free control method based on reinforcement learning. The method uses Q-learning to find optimal control strategies based on the reward feedback from the environment that maximizes its performance. The optimal control strategies are recorded in a Q-table and then employed to implement controllers. The advantage of the method is that it does not require an explicit knowledge of the system, target states, and unstable periodic orbits. All that we need is the parameters that we are trying to control and an unknown simulation model that represents the interactive environment. To control the FK model, we employ the perturbation policy on two different kinds of parameters, i.e., the pendulum lengths and the phase angles. We show that both of the two perturbation techniques, i.e., changing the lengths and changing their phase angles, can suppress chaos in the system and make it create the periodic patterns. The form of patterns depends on the initial values of the angular displacements and velocities. In particular, we show that the pinning control strategy, which only changes a small number of lengths or phase angles, can be put into effect.

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