| 1. |
- Ahlström, Christer, et al.
(författare)
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Chaotic dynamics of respiratory sounds
- 2006
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 29:5, s. 1054-1062
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Tidskriftsartikel (refereegranskat)abstract
- There is a growing interest in nonlinear analysis of respiratory sounds (RS), but little has been done to justify the use of nonlinear tools on such data. The aim of this paper is to investigate the stationarity, linearity and chaotic dynamics of recorded RS. Two independent data sets from 8 + 8 healthy subjects were recorded and investigated. The first set consisted of lung sounds (LS) recorded with an electronic stethoscope and the other of tracheal sounds (TS) recorded with a contact accelerometer. Recurrence plot analysis revealed that both LS and TS are quasistationary, with the parts corresponding to inspiratory and expiratory flow plateaus being stationary. Surrogate data tests could not provide statistically sufficient evidence regarding the nonlinearity of the data. The null hypothesis could not be rejected in 4 out of 32 LS cases and in 15 out of 32 TS cases. However, the Lyapunov spectra, the correlation dimension (D2) and the Kaplan-Yorke dimension (DKY) all indicate chaotic behavior. The Lyapunov analysis showed that the sum of the exponents was negative in all cases and that the largest exponent was found to be positive. The results are partly ambiguous, but provide some evidence of chaotic dynamics of RS, both concerning LS and TS. The results motivate continuous use of nonlinear tools for analysing RS data. © 2005 Elsevier Ltd. All rights reserved.
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| 2. |
- Allen, M. R., et al.
(författare)
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Dimensions of fractals in the large
- 2007
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier. - 0960-0779 .- 1873-2887. ; 31:1, s. 5-13
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Tidskriftsartikel (refereegranskat)
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| 3. |
- Cánovas, José S, et al.
(författare)
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A Method for Studying Non-Autonomous Affine Maps: An Application to a Two-Region Business Cycle Model
- 2007
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 34:4, s. 1285-1298
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Tidskriftsartikel (refereegranskat)abstract
- This paper is devoted to the study of the dynamics of a non-autonomous affine system. We apply the results to a two-region business cycle model of the Samuelson [Interactions between the multiplier analysis and the principle of acceleration. Rev Econ Statist 1939;21:75-8] multiplier-accelerator type.
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| 4. |
- Cánovas, José S, et al.
(författare)
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The Cournot-Theocharis Problem Reconsidered
- 2008
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 37:4, s. 1025-1039
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Tidskriftsartikel (refereegranskat)abstract
- In 1959 Theocharis [Theocharis RD. On the stability of the Cournot solution on the oligopoly problem. Review of economic Studies 1959;27:133–4] showed that with linear demand and constant marginal costs Cournot equilibrium is destabilized when the competitors become more than three. With three competitors the Cournot equilibrium point becomes neutrally stable, so, even then, any perturbation throws the system into an endless oscillation. Theocharis’s argument was in fact proposed already in 1939 by Palander [Palander T. Konkurrens och marknadsjämvikt vid duopol och oligopol. Ekonomisk Tidskrift 1939;41:124–45, 222–50]. None of these authors considered the global dynamics of the system, which necessarily becomes nonlinear when consideration is taken of the facts that prices, supply quantities, and profits of active firms cannot be negative. In the present paper, we address the global dynamics.
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| 5. |
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| 6. |
- Kalisch, Henrik, et al.
(författare)
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Numerical study of traveling-wave solutions for the Camassa-Holm equation
- 2005
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 25:2, s. 287-298
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Tidskriftsartikel (refereegranskat)abstract
- We explore numerically different aspects of periodic traveling-wave solutions of the Camassa-Holm equation. In particular, the time evolution of some recently found new traveling-wave solutions and the interaction of peaked and cusped waves is studied.
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| 7. |
- Karlberg, Magnus
(författare)
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Investigation of a saddle node bifurcation due to loss of contact in preloaded spherical roller thrust bearings
- 2009
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 41:4, s. 1750-1759
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Tidskriftsartikel (refereegranskat)abstract
- Spherical roller thrust bearings are used as supports in many rotating machineries. By applying an axial preload, clearance between the raceways and the rollers can be avoided. In order to increase the endurance, the preload shall be kept as low as possible. However, a bearing with low preload is sensitive of loosing full contact leading to nonlinear stiffness characteristics. The objective of this paper is to suggest a tool, which can be used to determine suitable preload and to show that a saddle node bifurcation can occur if the preload is too small.Studying the model in a rotating frame leads to an autonomous equation of motion from which stationary points and their stability can be analysed. Some set of parameters give a nonhyperbolic eigenvalue, and by investigating the corresponding central manifold it is found that a saddle node bifurcation occurs. Since explicit equations for the stationary points are derived, they can be used to choose a preload high enough to make sure that full contact always is a possible solution. It is however shown that if the preload becomes too small, the system enters an area of multiple solutions and a saddle node bifurcation can occur.
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| 8. |
- Khrennikov, Andrei, 1958-
(författare)
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Gene expression from polynomial dynamics in the2-adic information space
- 2009
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier. - 0960-0779 .- 1873-2887. ; 42:1, s. 341-347
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Tidskriftsartikel (refereegranskat)abstract
- We perform geometrization of genetics by representing genetic information by points of the 4-adic information space. By well known theorem of number theory this space can also be represented as the 2-adic space. The process of DNA-reproduction is described by the action of a 4-adic (or equivalently 2-adic) dynamical system. As we know, the genes contain information for production of proteins. The genetic code is a degenerate map of codons to proteins. We model this map as functioning of a polynomial dynamical system. The purely mathematical problem under consideration is to find a dynamical system reproducing the degenerate structure of the genetic code. We present one of possible solutions of this problem.
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| 9. |
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| 10. |
- Lindström, Torsten
(författare)
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Detecting chaos requires careful analysis of nearly periodic data
- 2009
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Ingår i: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 42:1, s. 212-223
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Tidskriftsartikel (refereegranskat)abstract
- We show that models fitted to data in many cases fit unstable periodic solutions in attracting periodic solutions of the 'true model' that generated the data. An attracting solution containing the neighborhood of the fitted unstable solution in its domain of attraction may possess entirely different dynamical properties. Thus, an attracting chaotic solution with positive Lyapunov exponent may describe periodic solutions with negative Lyapunov exponents and vice versa. These problems can in principle be remedied, if the fitted models would be allowed to contain an arbitrary complexity and if an infinite amount of data would be available. We claim that we stay far from such limits in ecology, for instance. Therefore, we think our approach is essential to bear in mind when making data-based predictions concerning dynamical behavior. Our general conclusion is that less data is required in nearly periodic cases than in chaotic cases for rejecting models not allowing complex behavior.
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