Chian, Abraham C.-L.; Borotto, Felix A.; Rempel, Erico L.; Rogers, Colin Attractor merging crisis in chaotic business cycles. (English) Zbl 1081.37058 Chaos Solitons Fractals 24, No. 3, 869-875 (2005). The present paper shows that chaotic transitions, such as the attractor merging crisis, are a fundamental feature of nonlinear business cycles. The crisis diagram for the attractor merging crises is studied, which summarizes the system dynamics leading to the onset of crisis. The onset of an attractor merging crisis is characterized using the tools of unstable periodic orbits and their associated stable and unstable manifolds. Mathematical modelling presented in the paper of crisis can deepen our understanding of sudden major changes of economic variables often encountered in business cycles. Reviewer: Messoud A. Efendiev (Berlin) Cited in 32 Documents MSC: 37N40 Dynamical systems in optimization and economics 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 37C27 Periodic orbits of vector fields and flows 91B62 Economic growth models 37C70 Attractors and repellers of smooth dynamical systems and their topological structure Keywords:chaotic business cycles; attractor; unstable periodic orbits; stable and unstable manifolds PDF BibTeX XML Cite \textit{A. C. L. Chian} et al., Chaos Solitons Fractals 24, No. 3, 869--875 (2005; Zbl 1081.37058) Full Text: DOI References: [1] Gabisch, G.; Lorenz, H.W., Business cycle theory: a survey of methods and concepts, (1987), Springer-Verlag Berlin [2] Puu, T., Nonlinear economic dynamics, (1989), Springer-Verlag Berlin · Zbl 0695.90002 [3] Lorenz, H.W., Nonlinear dynamical economics and chaotic motion, (1989), Springer-Verlag Berlin · Zbl 0717.90001 [4] Goodwin, R.M., Chaotic economic dynamics, (1990), Clarendon Press Oxford [5] Gandolfo, G., Economic dynamics, (1997), Springer-Verlag Berlin [6] Mosekilde, E.; Larsen, E.R.; Sterman, J.D.; Thomsen, J.S., Nonlinear mode-interaction in the macroeconomy, Ann. oper. res., 37, 185-215, (1992) · Zbl 0800.90147 [7] Szydlowski, N.; Krawiec, A.; Tobola, J., Nonlinear oscillations in business cycle model with time lags, Chaos, solitons, & fractals, 12, 505-517, (2001) · Zbl 1036.91038 [8] Puu, T.; Sushko, I., A business cycle model with cubic nonlinearity, Chaos, solitons, & fractals, 19, 597-612, (2004) · Zbl 1068.91054 [9] Grebogi, C.; Ott, E.; York, J.A., Crises, sudden changes in chaotic attractors, and transient chaos, Physica D, 7, 181-200, (1983) [10] Grebogi, C.; Ott, E.; Romerias, F.; Yorke, J.A., Critical exponents for crisis-induced intermittency, Phys. rev. A, 36, 5365-5380, (1987) [11] Chian, A.C.L.; Borotto, F.A.; Rempel, E.L., Alfvén boundary crisis, Int. J. bifurcat. chaos, 12, 1653-1658, (2002) · Zbl 1051.76071 [12] Chian, A.C.L.; Rempel, E.L.; Macau, E.E.; Rosa, R.R.; Christiansen, F., High-dimensional interior crisis in the Kuramoto-Sivashinsky equation, Phys. rev. E, 65, 035203(R), (2002) [13] Borotto, F.A.; Chian, A.C.L.; Rempel, E.L., Alfvén interior crisis, Int. J. bifurcat. chaos, 14, 2375-2380, (2004) · Zbl 1069.76059 [14] Chian, A.C.L., Nonlinear dynamics and chaos in macroeconomics, Int. J. theoret. appl. finan., 3, 601, (2001) [15] Wolf, A.; Swift, J.B.; Swinney, H.L.; Vastano, J.A., Determining Lyapunov exponents from a time series, Physica D, 16, 285-317, (1985) · Zbl 0585.58037 [16] Parker, T.S.; Chua, L.O., Practical numerical algorithms for chaotic systems, (1989), Springer-Verlag New York · Zbl 0692.58001 [17] Ott, E., Chaos in dynamical systems, (1993), Cambridge University Press Cambridge · Zbl 0792.58014 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.