Commun Nonlinear Sci Numer Simulat Research Articles

Comment on “Topology identification and adaptive synchronization of uncertain complex networks with adaptive double scaling functions” [Commun Nonlinear Sci Numer Simulat 16 (2011) 3337

We slightly modify definition in paper [Xu Y, Zhou W, Fang J, Sun W. Topology identification and adaptive synchronization of uncertain complex networks with adaptive double scaling functions. Commun Nonlinear Sci Numer Simulat 2011;16:3337–3343], so remark stated problem is resolved in paper [1]. Finally, a more general theorem is given.

Using delayed damping to minimize transmitted vibrations

In Mokni et al. [Mokni L, Belhaq M, Lakrad F. Effect of fast parametric viscous damping excitation on vibration isolation in sdof systems. Commun Nonlinear Sci Numer Simulat 2011;16:1720–1724], it was shown that in a single degree of freedom system a fast nonlinear parametric damping enhances vibration isolation with respect to the case where the nonlinear damping is time-independent. The present work proposes additional enhancement of vibration isolation using delayed nonlinear damping. Attention is focused on assessing the contribution of a delayed nonlinear damping over a fast parametric damping in terms of minimizing transmissibility. The results show that a nonlinear damping with delay greatly improves vibration isolation.

Comments on “Fuzzy fractional order sliding mode controller for nonlinear systems” [Commun Nonlinear Sci Numer Simulat 15 (2010) 963–978

The aim of this note is to point out some comments to the article [Delavari H, Ghaderi R, Ranjbar A, Momani S. Fuzzy fractional order sliding mode controller for nonlinear systems, Commun Nonlinear Sci Numer Simulat 15 (2010) 963–978].

Comments on “Design of sliding mode controller for a class of fractional-order chaotic systems” [Commun Nonlinear Sci Numer Simulat 17 (2012) 356–366

Some comments on the paper [Yin C, Zhong S-M, Chen W-F. Design of sliding mode controller for a class of fractional-order chaotic systems. Commun Nonlinear Sci Numer Simulat 17 (2012) 356–366] are pointed out in this note. Besides, recently introduced fractional-order Lyapunov stability theorems are used to prove the finite-time occurrence of the sliding motion.

On a problem of iteration invariants for distributional chaos

We show that if f is a DC3 continuous map of a compact metric space then also f N is DC3, for every N > 0. This solves a problem given by [Li R. A note on the three versions of distributional chaos. Commun Nonlinear Sci Numer Simulat 2011;16:1993–1997].

Collision analysis of a chaos-based hash function with both modification detection and localization capability

The collision problem of a chaos-based hash function with both modification detection and localization capability is investigated [Xiao D, Shih FY, Liao XF. A chaos-based hash function with both modification detection and localization capabilities. Commun Nonlinear Sci Numer Simulat 2010;15(9):2254–61]. The simulation gives the same detection and localization hash values for distinct messages. The expense of the birthday attack on the hash function is far less than expected. The certain symmetries of message distribution may result in the same detection hash value for distinct messages.

Enhanced preliminary group classification of a class of generalized diffusion equations

The method of preliminary group classification is rigorously defined, enhanced and related to the theory of group classification of differential equations. Typical weaknesses in papers on this method are discussed and strategies to overcome them are presented. The preliminary group classification of the class of generalized diffusion equations of the form u t = f ( x , u ) u x 2 + g ( x , u ) u xx is carried out. This includes a justification for applying this method to the given class, the simultaneous computation of the equivalence algebra and equivalence (pseudo) group, as well as the classification of inequivalent appropriate subalgebras of the whole infinite-dimensional equivalence algebra. The extensions of the kernel algebra, which are induced by such subalgebras, are exhaustively described. These results improve those recently published in Commun Nonlinear Sci Numer Simul.

On an approximate method for the delay logistic equation

This note concerns with the asymptotic properties of solutions of the delay logistic equation. In particular, we point out some false statements in the recent paper Khan et al. [Khan H, Liao SJ, Mohapatra RN, Vajravelu K. An analytical solution for a nonlinear time-delay model in biology. Commun Nonlinear Sci Numer Simulat 2009;14:3141–3148]. Moreover, we show that the author’s method is not able to reveal the basic and important features of the dynamics of the delay logistic equation, and gives misleading results.

Complement to ‘Second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties’ [Commun Nonlinear Sci Numer Simulat 15 (2010) 3241–3247

Owing to the singularity problem having not been considered in control design process, we present some points to improve the results of paper [Wei Xiang, Yugao Huangpu, second-order terminal sliding mode controller for a class of chaotic systems with unmatched uncertainties, Commun Nonlinear Sci Numer Simulat 15 (2010) 3241–3247].

Comments on “Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control” [Commun Nonlinear Sci Numer Simulat 2010;15:3754–3762

In this note some points to paper [L. Pan, W. Zhou, J. Fang, D. Li, Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control, Commun Nonlinear Sci Numer Simulat 2010;15:3754–3762] are presented. Hereby, we illustrate that the way that authors in [1] treat with fractional version of Lyapunov stability theorem suffers lack of a correct justification.

Comment on “A note on a study on an integrable system of coupled KdV equations”

We analyze the note by Muraved [A note on A study on an integrable system of coupled KdV equations [1], Commun Nonlinear Sci Numer Simulat. doi:10.1016/j.cnsns.2010.06.018]. Author tried to show that our approach is curious. We demonstrate that, author has not shown any error and presented a curious note.

A note on “A study on an integrable system of coupled KdV equations”

We analyze the paper by Wazwaz [Wazwaz AM. A study on an integrable system of coupled KdV equations. Commun Nonlinear Sci Numer Simul, 2010;15:2846–2850]. Author tried to show that the system of coupled KdV equations is completely integrable but he has used the curious approach for the proof. We demonstrate that, author has taken the relation between dependent variables and has obtained the well known result by Hirota for the KdV equation.

Comment on “Based on interval type-2 adaptive fuzzy H∞ tracking controller for SISO time-delay nonlinear systems”

In this comment, we point out the inappropriateness of Theorem 1 in the article [Tsung-Chih Lin, Mehdi Roopaei. Based on interval type-2 adaptive fuzzy H ∞ tracking controller for SISO time-delay nonlinear systems. Commun Nonlinear Sci Numer Simulat 2010;15:4065–75]. For solving this problem, some formular mistakes are corrected and novel parameter adaptive laws of interval type-2 fuzzy neural network system are given.

Comment on: “Linear observer based projective synchronization in delay Rössler system”, Dibakar Ghosh, Papri Saha, A. Roy Chowdhury [Commun Nonlinear Sci Numer Simul 15 (2010) 1640–1647

In this note, we present some points to paper Dibakar et al., 2010 [1].

Comments on: “Synchronization of N-coupled fractional-order chaotic systems with ring connection” [Commun Nonlinear Sci Numer Simulat 2010;15:401–12

In this note, we present some points to paper [Tang Yang, Fang Jian-an, Synchronization of N-coupled fractional-order chaotic systems with ring connection. Commun Nonlinear Sci Numer Simulat 2010;15:401–12].

Modified substitution–diffusion image cipher using chaotic standard and logistic maps

Recently Patidar et al. [Commun Nonlinear Sci Numer Simulat 14;2009:3056–75] proposed a new substitution–diffusion image cipher using chaotic standard and logistic maps, which is very fast and possess all the confusion and diffusion properties that any good cryptosystem should have. Soon after the proposal, Rhouma et al. [Commun Nonlinear Sci Numer Simulat 2010;15:1887–92.] proposed an equivalent description of the PPS09 cryptosystem which facilitated them in the cryptanalysis of the original cipher in terms of chosen plainext and known plaintext attacks. In this paper, we propose modifications in the Patidar et al.’s image cipher to make it robust against these two cryptanalytic attacks. The security analysis shows that the modified image cipher preserves all the good properties of the original cipher and is also capable to stand against the aforesaid attacks.

Homoclinical structure of the chaotic attractor

In the reference [Akhmet MU. Devaney chaos of a relay system. Commun Nonlinear Sci Numer Simulat 2009;14:1486–93.], a relay system was introduced, which admits a chaotic attractor with Devaney’s ingredients. Now, we prove that the attractor consists of homoclinic solutions. A simulation of the attractor is provided for a pendulum equation. Similar results for impulsive differential equations were announced in the plenary talk [Akhmet MU. Hyperbolic sets of impact systems. Dyn Contin Discrete Impuls Syst Ser A Math Anal 2008;15(Suppl. S1):1–2. Proceedings of the 5th international conference on impulsive and hybrid dynamical systems and applications, Beijin: Watan Press; 2008.].

A note on the use of modified Adomian decomposition method for solving singular boundary value problems of higher-order ordinary differential equations

This paper extend the work [Yahya Qaid Hasan, Liu Ming Zhu. Solving singular boundary value problems of higher-order ordinary differential equations by modified Adomian decomposition method. Commun Nonlinear Sci Numer Simul. doi :10.1016/j.cnsns.2008.09.027] to high order of singular boundary value problems. Solution of these problems is considered by proposed modification of Adomian decomposition method. The proposed method can be applied to linear and nonlinear problems. Some examples are presented to show the ability of the method for linear and non-linear ordinary differential equation.

Effects of variable viscosity in a third grade fluid with porous medium: An analytic solution

This study extends the analysis of ref. [Hayat T, Ellahi R, Asghar S. The influence of variable viscosity and viscous dissipation on the non-Newtonian flow: An analytic solution, Commun Nonlinear Sci Numer Simul 2007;12:300–313] in a porous medium by employing modified Darcy’s law. Beside this Reynolds and Vogels models of temperature dependent viscosity are considered. The problem is solved using homotopy analysis method (HAM). Expressions of velocity and temperature profiles are constructed analytically and explained with the help of graphs.

Comment on “Lie group analysis of radiation natural convection flow past an inclined surface”, S. Sivasankaran, M. Bhuvaneswari, P. Kandaswamy, E.K. Ramasami [Commun Nonlinear Sci Numer Simul 2008;13:269–76

Comment on “Lie group analysis of radiation natural convection flow past an inclined surface”, S. Sivasankaran, M. Bhuvaneswari, P. Kandaswamy, E.K. Ramasami [Commun Nonlinear Sci Numer Simul 2008;13:269–76