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References
Afraimovich, V.S., Shil’nikov, L.P., 1983, “Invariant two-dimensional tori, their destruction and stochasticity”, Gorkii University, Gorkii, Russia, pp. 3–26.
Aronson, D.G., Chory, M.A., Hall, G.R., McGehee, R.P., 1982, “Bifurcations from an invariant circle for two-parameter families of maps of the plane: A computer-assisted study”, Commun. Math. Phys. 83, pp. 303–354.
Banerjee, S., Ranjan, P., Grebogi, C, 2000, “Bifurcations in Two-Dimensional Piecewise Smooth Maps-Theory and Applications in Switching Circuits”, IEEE Trans. Circuits Syst.-I: Fund. Theory Appl. 47 No. 5, pp. 633–643.
Boyland, P.L., 1986, “Bifurcations of circle maps: Arnol’d tongues, instability and rotation intervals”, Commun. Math. Phys., 106, pp. 353–381.
Guckenheimer, J., Holmes, P., 1983, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag.
Gumovski, I., Mira. C, 1980, Recurrences and Discrete Dynamical Systems. Springer-Verlag.
Hao Bai-Lin, 1989, Elementary Symbolic Dynamics and Chaos in Dissipative Systems. World Scientific, Singapore.
Hommes, C.H., 1991, Chaotic dynamics in economic models. Wolters-Noodhoff, Groningen.
Hommes, C.H., Nusse, H., 1991, “Period three to period two bifurcations for piecewise linear models”, Journal of Economics 54(2), pp. 157–169.
Kuznetsov, Y., 1995, Elements of applied bifurcation theory. Springer-Verlag.
Maistrenko, Y., Sushko, I., Gardini, L., 1998, “About two mechanisms of reunion of chaotic attractors”, Chaos, Solitons & Fractals, 9(8), pp. 1373–1390.
Mira, C, Gardini, L., Barugola, A., Cathala, J.C., 1996, Chaotic dynamics in two-dimensional noninvertible maps. Singapore, World Scientific.
Nusse, H.E., Yorke, J.A., 1992, “Border-collision bifurcations including “period two to period three” for piecewise smooth systems”, Physica D, 57, pp. 39–57.
Sushko, I., Puu, T., Gardini, L., 2003, “The Hicksian floor-roof model for two regions linked by interregional trade”, Chaos Solitons & Fractals, 18, pp. 593–612.
Zhusubaliyev, Z.T., Mosekilde, E., 2003, Bifurcations and Chaos in Piecewise-Smooth Dynamical Systems, Singapore, World Scientific.
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Sushko, I., Gardini, L. (2006). Center Bifurcation for a Two-Dimensional Piecewise Linear Map. In: Puu, T., Sushko, I. (eds) Business Cycle Dynamics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32168-3_3
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DOI: https://doi.org/10.1007/3-540-32168-3_3
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