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1.
We have considered a chemostat model with two distributed delays in a recent paper [Chaos, Solitons & Fractals 2004;20:995–1004], where, using the average time delay corresponding to the growth response as a bifurcation parameter, it is proven that the model undergoes Hopf bifurcations for two weak kernels. This article is a sequel to the previous work. The direction and stability of the bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. The results are consistent with the numerical results in [Chaos, Solitons & Fractals 2004;20:995–1004].  相似文献   

2.
Recently, the concept of intuitionistic fuzzy normed spaces was introduced by Saadati and Park [Saadati R, Park JH. Chaos, Solitons & Fractals 2006;27:331–44]. Karakus et al. [Karakus S, Demirci K, Duman O. Chaos, Solitons & Fractals 2008;35:763–69] have quite recently studied the notion of statistical convergence for single sequences in intuitionistic fuzzy normed spaces. In this paper, we study the concept of statistically convergent and statistically Cauchy double sequences in intuitionistic fuzzy normed spaces. Furthermore, we construct an example of a double sequence to show that in IFNS statistical convergence does not imply convergence and our method of convergence even for double sequences is stronger than the usual convergence in intuitionistic fuzzy normed space.  相似文献   

3.
We point out that Proposition 3.1 in [E. Petrisor. Reconnection scenarios and the threshold of reconnection in the dynamics of non-twist maps. Chaos Solitons Fractals 2002;14(1):117–27] is, strictly speaking, false. On the other hand, we suggest that for near integrable mappings, the results of [E. Petrisor. Reconnection scenarios and the threshold of reconnection in the dynamics of non-twist maps. Chaos Solitons Fractals 2002;14(1):117–27] are qualitatively correct and quantitatively very approximate.  相似文献   

4.
We consider a simple population model which includes time-dependent parameters prompted by the recent work of Lakshmi [Chaos, Solitons & Fractals 16 (2003) 183]. Time-dependent parameters introduce the possibility of chaos into the dynamics of even simple models. We provide some solutions of the model, compare them with the ones obtained by Lakshmi and discuss their behaviour and properties.  相似文献   

5.
In the present work, first we give some definitions and theorems on hyperbolic maps, structurally stability and deterministic chaos. The limit set of the Kleinian transformation acting on the E-infinity Cantorian space–time turned out to be a set of periodic continued fractions as shown in [Chaos, Solitons & Fractals, 21 (2004) 9]. That set has a hyperbolic structure and is structurally stable. Subsequently, we show that the appearance of transversal homoclinic points induces a chaotic behavior in that set.  相似文献   

6.
A modified variable-coefficient projective Riccati equation method is proposed and applied to a (2 + 1)-dimensional simplified and generalized Broer–Kaup system. It is shown that the method presented by Huang and Zhang [Huang DJ, Zhang HQ. Chaos, Solitons & Fractals 2005; 23:601] is a special case of our method. The results obtained in the paper include many new formal solutions besides the all solutions found by Huang and Zhang.  相似文献   

7.
We present a so-called zero-crossing identification method that can crack the security shell of the chaotic encryption method [Chaos, Solitons & Fractals 19 (2004) 919] with periodic modulation. By collecting a special set of truncated data from the zero-crossing incidents of the modulated signal, we can detect the modulating function from chaotic signal. Furthermore we extend the technique to extract modulating function from noise and discuss the potential applications of this method in engineering.  相似文献   

8.
The goal of this work is to determine classes of traveling solitary wave solutions for a differential approximation of a discontinuous Galerkin finite difference scheme by means of an hyperbolic ansatz. It is shown that spurious solitary waves can occur in finite-difference solutions of nonlinear wave equation. The occurence of such a spurious solitary wave, which exhibits a very long life time, results in a non-vanishing numerical error for arbitrary time in unbounded numerical domain. Such a behavior is referred here to have a structural instability of the scheme, since the space of solutions spanned by the numerical scheme encompasses types of solutions (solitary waves in the present case) that are not solutions of the original continuous equations. This paper extends our previous work about classical schemes to discontinuous Galerkin schemes (David and Sagaut in Chaos Solitons Fractals 41(4):2193?C2199, 2009; Chaos Solitons Fractals 41(2):655?C660, 2009).  相似文献   

9.
Assessing the markets perception of future interest and inflation rate volatility is of crucial importance to assess the evolution of expectations in an inflation targeting framework. This article aims to evaluate the information content of implied volatilities extracted from a Brazilian interest-rate call option. We compared the predictive performance of three different approaches: one using the traditional [Black F. The pricing of commodity contracts. J Financ Econ 1976;3:167–79] method, another one using the extended-Vasicek model, and in the third approach, we use a GARCH(2, 1) model. The empirical evidence was more favorable to the extended-Vasicek method. Moreover, extended-Vasicek’s implied volatilities could predict around 33% (adjusted R2) of the variations in realized volatility. Further research could test for the predictive content of long memory options such as those suggested in Wang et al. [Wang X-T, Qiu W-Y, Ren F-Y. Option pricing of fractional version of the Black–Scholes model with Hurst exponent H being in . Chaos, Solitons & Fractals 2001;12:599–608; Wang X-T, Ren F-Y, Liang X-Q. A fractional version of the Merton model. Chaos, Solitons & Fractals 2003;15:455–63].  相似文献   

10.
In this paper, new explicit exact soliton-like solutions and multi-sliton solutions to the (2+1) dimensional Burgers equation are obtained by using the further extended tanh method [Phys Lett A 307 (2003) 269, Chaos, Solitons & Fractals 17 (2003) 669]. Based on the derived exact solutions which contain arbitrary functions, special soliton-like structures are revealed.  相似文献   

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