| 1. |
- Agliari, Anna, et al.
(author)
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The dynamics of a triopoly Cournot game
- 2000
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In: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 11:15, s. 2531-2560
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Journal article (peer-reviewed)abstract
- This paper reconsiders the Cournot oligopoly (noncooperative) game with iso-elastic demand and constant marginal costs, one of the rare cases where the reaction functions can be derived in closed form. It focuses the case of three competitors, and so also extends the critical line method for non-invertible maps to the study of critical surfaces in 3D. By this method the various bifurcations of the attractors and their basins are studied. As a special case the restriction of the map to an invariant plane when two of the three firms are identical is focused.
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| 2. |
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| 3. |
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| 4. |
- Dankowicz, H., et al.
(author)
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Low-velocity impacts of quasiperiodic oscillations
- 2002
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In: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 14:2, s. 241-255
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Journal article (peer-reviewed)abstract
- A method based on the idea of a discontinuity mapping is derived for predicting the characteristics of system attractors that occur following a grazing intersection of a two-frequency, quasiperiodic oscillation with a two-dimensional impact surface in a three-dimensional state space. Within certain restrictions, the correction to the non-impacting flow afforded by the discontinuity mapping is computable using quantities determined solely by the non-impacting flow and the properties of the impact surface and the associated impact mapping in the immediate vicinity of the initial grazing contact. A model example is discussed to illustrate the quantitative predictive power of the discontinuity-mapping approach even relatively far away in parameter space from the original grazing intersection. Finally, constraints on the applicability of the methodology are described in detail with suggestions for suitable modifications.
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| 5. |
- Jerrelind, Jenny, et al.
(author)
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Nonlinear dynamics of parts in engineering systems
- 2000
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In: Chaos, Solitons & Fractals. - : Elsevier. - 0960-0779 .- 1873-2887. ; 11:15, s. 2413-2428
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Journal article (peer-reviewed)abstract
- By definition, chaotic vibrations arise from nonlinear deterministic physical systems or non-random differential or difference equations. In numerous engineering systems there exist nonlinearities which might affect the dynamic behaviour of the system. The objectives in this work are to summarise previous work on nonlinear dynamics of engineering parts and products and to investigate if research on how nonlinear parts can effect the total behaviour of the products have been performed. It is found that common nonlinear parts are machine elements such as gears, bearings, brakes and suspension systems. The most studied part in a product is of impact hammer type. The products are ordinary products, from searing machines, drilling machines and printers to railway vehicles. In order to be able to design reliable products the methodology should be further developed to enable use by engineers. One can conclude that the effect of nonlinear parts on the total system behaviour is still a fairly uninvestigated area.
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| 6. |
- Johansson, Börje, et al.
(author)
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Self-organised adjustments in a market with price-setting firms
- 2003
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In: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 18:3, s. 463-475
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Journal article (peer-reviewed)abstract
- The model depicts a single market where firms select prices every new transaction date. The customers, who are input-purchasing firms, decide every new date how much to buy from each supplier. The optimisation decisions of customers are based on price information and are, in addition, influenced by adjustment costs associated with changing the amount ordered (purchased) from each supplier. It is shown that such a market can have a stable equilibrium even when the product sold on the market is completely homogenous. Moreover, the solution is compatible with U-shaped, decreasing and increasing costs of the supplying firms. The main result is that if the transaction inertia is sufficiently strong, it will stabilise the market adjustment process. In equilibrium the market has a self-organised structure of transactions.
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| 7. |
- Karlberg, Magnus, et al.
(author)
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Investigation of an unbalanced rotor system with bearing clearance and stabilising rods
- 2004
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In: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 20:2, s. 363-374
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Journal article (peer-reviewed)abstract
- The nonlinear vibrations of a rotor system with bearing clearance and stabilising rods are considered. In this paper the main objective is to evaluate effects of applying stabilising rods and from a dynamical point of view find preferable parameter ranges. A piecewise linear two degrees-of-freedom model is proposed. The system is studied and evaluated by analysis of steady state, bifurcation diagrams, Lyapunov exponents and contact force. It is shown how transition lines (which separate different categories of motion), periodicity and sensitivity to small perturbation are affected by the parameters defining the stability rods. By applying specific stabilising rods the periodicity is changed for some parameter ranges, unstable areas are reduced, the total maximum normal contact force is increased while the dynamical part is mainly reduced. The analytical expressions for the transition limits can be used as a design tool to choose suitable parameters. It is concluded that the stability rods should be applied vertically and that high preloading and stiffness prevents the system from impact motion. The stabilising rods are effective tools to avoid nonlinear behaviors but it is necessary to carefully analyse the specific application
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| 8. |
- Karlberg, Magnus, et al.
(author)
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Numerical investigation of an unbalanced rotor system with bearing clearance
- 2003
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In: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 18:4, s. 653-664
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Journal article (peer-reviewed)abstract
- The nonlinear vibrations of a rotor system with bearing clearance are considered. The model consists of an unbalanced shaft with two d.o.f connected to a nonrotating massless housing by linear springs and dashpots. The clearance occurs when the housing (modelled as a ring) has a radius less than the stator. The behaviour of this system has been investigated with the use of time histories, Poincare maps, bifurcation diagrams, Lyapunov exponents, phase portraits, cell mapping and design space. Numerical simulations have achieved these results. The main objective was to find possible causes of failure in machines containing this type of clearance. The existence of subharmonic, quasi-periodic or even possible chaotic motion has been found. It is shown that these motions may give raise to bouncing modes, which results in high bearing forces and hence can be a possible cause of failure
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| 9. |
- Puu, Tönu, 1936-, et al.
(author)
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A business cycle model with cubic nonlinearity
- 2004
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In: Chaos, Solitons & Fractals. - 0960-0779 .- 1873-2887. ; 19:3, s. 597-612
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Journal article (peer-reviewed)abstract
- This paper deals with a simple multiplier-accelerator model of the business cycle, including a cubic nonlinearity. The corresponding two dimensional iterative map is represented in terms of its bifurcation diagram in parameter space. A number of bifurcation sequences for attractors and their basins are studied.
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| 10. |
- Puu, Tönu, 1936-
(author)
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Chaos in business cycles
- 1991
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In: Chaos, Solitons & Fractals. - : Elsevier BV. - 0960-0779 .- 1873-2887. ; 1:5, s. 457-473
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Journal article (peer-reviewed)abstract
- The business cycle is studied in terms of the mapping Zt = λZt−1 − (λ+1)Z3t−1 − σYt−1 Yt = Zt−1 + Y−1 where the variables Y, Z denote income and rate of income change respectively, and λ, σ are two structural parameters. The model produces chaotic or periodic output for income differences. For small σ income acts as a slow feed back causing bifurcations between periodic and chaotic behaviour over the cycle. Typically, transitions between prosperity and depression set in with chaos after which there follows a period halving route to order.
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