Erratum: Characteristics of chaos evolution in one-dimensional disordered nonlinear lattices [Phys. Rev. E 98 , 052229 (2018)]

Abstract

We have identified, in the original paper, confusing use of the symbol ξ l denoting the normalized energy [disordered Klein-Gordon (DKG) system] and norm density [disordered discrete nonlinear Schrödinger equation (DDNLS)], which only affects the presentation of some of the provided information about the setup of our numerical simulations. Thus, the following changes should be made in the first paragraph of Sec. III: (a) p l = ± √ 2ξ l should become p l = ± √ 2ξ l H K (line 4), (b) ξ l = 1 should become ξ l S = 1 (line 7), and (c) H K = Lξ l should become H K (line 11). Furthermore, in the last entry of the presentation of the studied cases in Sec. III A, ξ l should become ξ l H K for the DKG system and ξ l S for the DDNLS model

Heterogeneity and chaos in the Peyrard-Bishop-Dauxois DNA model

“…The DVD gives a measure of the sensitivity of a certain region of the chain to small variations of initial conditions, and provides some idea of the 'strength of the nonlinearity' at each site as the system evolves [41,42].…”

“…regions of high ξ i (Eq. 3) values, in chaotic, nonlinear lattices [41,42]. In this section we examine the spatiotemporal evolution of such DVDs in conjunction with the displacements of the system.…”

Properties of Normal Modes in a Modified Disordered Klein-Gordon Lattice: From Disorder to Order

“…, N , with l A 2 ν,l = 1, are the system's NMs and the eigenvalues ω 2 ν are the corresponding squared frequencies of these modes. The dynamics of the nonlinear version (DKG) of system (1) obtained by the presence of an additional nonlinear term in the on-site potential ( l q 4 l /4) has been extensively studied [7,13,[15][16][17], mainly in comparison with the DDNLS model, i.e. the nonlinear version of the LDSE…”

“…nearest-neighbor hopping) Anderson model with disorder on the on-site potentials [1,19]. We note that the DDNLS system studied in [7,13,[15][16][17] is obtained by the addition of the term β|ψ l | 4 /2 in (4), with β ≥ 0 quantifying the nonlinearity strength. The NMs of system (4) can be found by setting ψ l = A l exp(−iλt), which leads to the linear eigenvalue problem…”

“…On the other hand, the introduction of nonlinearities to such systems leads to the interaction of the NMs and the introduction of chaos. In general two typical one-dimensional (1D) disordered nonlinear lattices, namely the Klein-Gordon model (DKG) and the discrete nonlinear Schrödinger equation (DDNLS), have been at the center of studies of the effect of * E-mail: haris.skokos@uct.ac.za nonlinearity on AL [6][7][8][13][14][15][16][17]. In these works it was found that eventually nonlinearity destroys AL and the characteristics of different spreading behaviors (the so-called 'weak' and 'strong chaos' regimes) were identified.…”