Abstract
Financial stability is one of the most widely discussed issues in today’s economic literature. The relevance of analyses on financial stability was first recognized during the international financial crises at the end of the 90s, also strengthened by the financial and economic crisis emerging in 2007. Even if an economical system possesses deterministic characteristics, a chaotic behavior can occur in the financial system. Because of slight errors, chaotic dynamical systems can lead to completely different trajectories. Hence, the chaos control in the financial systems is required. In this paper, we analyze the stability of equilibria of a financial system described by three dynamic equations and apply stabilization techniques for the unstable equilibrium state of the system. Our results are essentially based on the Theorem of allotting the characteristic polynomial (see, e.g. [1], Theorem 2.2.3). We also suggest the use of optimal stabilization, by means of a quadratic loss-function.
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References
Halanay, A., Dragan, V.: Stabilization of Linear Systems. Birkhäuser, Switzerland (1999)
Hübler, A.: Adaptive control of chaotic systems. Helvetica Physica Acta 62, 343–346 (1989)
Ma, J., Chen, Y.: Study for the bifurcation topological structure and the global complicated character of a kind of non-linear finance system (I). Appl. Math. Mech. 22(11), 1240–1251 (2001)
Ma, J., Chen, Y.: Study for the bifurcation topological structure and the global complicated character of a kind of non-linear finance system (II). Appl. Math. Mech. 22(11), 1375–1382 (2001)
Cai, G., Huang, J.: A new finance chaotic attractor. Int. J. Nonlinear Sci. 3(3), 213–220 (2007)
Cai, G., Yu, H., Li, Y.: Stabilization of a modified chaotic finance system. In: 4th International Conference on Information and Computing, pp. 188–191. IEEE Press, New York (2011)
Chen, W.: Dynamics and control of a financial system with time-delayed feedbacks. Chaos Solitons Fractals 37(4), 1198–1207 (2008)
Ding, J., Yang, W., Yao, H.: A new modified hyperchaotic finance system and its control. Int. J. Nonlinear Sci. 8(1), 59–66 (2009)
Emiroğlu, S., Uyaroğlu, Y., Köklükaya, E.: Control of a chaotic finance system with passive control. In: 3rd International Symposium on Sustainable Development, Sarajevo, pp. 125–130. International Burch University, Sarajevo (2012)
Gelberi, H., Emiroğlu, S., Uyaroğlu, Y, Yalçin, M.A.: Time delay feedback control of chaos in a hyperchaotic finance system. In: 3rd International Symposium on Sustainable Development, Sarajevo, pp. 139–144. International Burch University, Sarajevo (2012)
Hou, Y.Y., Liau, B.Y., Chen, H.C.: Synchronization of unified chaotic systems using sliding mode controller. Math. Prob. Eng. 2012 (2012). Article 632712
Lukyanov, A.G., Utkin, V.I.: Methods of reducing equations for dynamic systems to a regular form. Autom. Remote Control 42(4), 413–420 (1981)
Rigatos, G.G.: State-Space Approaches for Modelling and Control in Financial Engineering. Springer, Cham (2017)
Sundarapandian, V., Sivaperumal, S.: Global chaos synchronization of hyperchaotic Chen system by sliding mode control. Int. J. Eng. Sci. Technol. 3(5), 4265–4271 (2011)
Uyaroğlu, Y., Temel, R., Kırlıoğlu, H.: Feedback control of chaos in a hyperchaotic finance system. In: 3rd International Symposium on Sustainable Development, Sarajevo, pp. 135–139. International Burch University, Sarajevo (2012)
Altăr-Samuel, A., Alupoaiei, A.: Dynamics in a New-Keynesian model with financial accelerator and uncertainty. In: Economic Computation and Economic Cybernetic Studies and Research, vol. 51. Editura Academia de Studii Economice, Bucharest (2017)
Azar, A.T., Sundarapandian, V.: Advances in Chaos Theory and Intelligent Control. Springer, Cham (2016)
Azar, A.T., Zhu, Q.: Advances and Applications in Sliding Mode Control. Springer, Cham (2015)
Acknowledgement
This work was supported by a grant of the Romanian National Authority for Scientific Research, CNCS – UEFISCDI, project number PN-II-RU-TE-2014-2499 entitled “Coordinating Monetary and Macroprudential Policies”.
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Altăr-Samuel, A. (2019). Chaos and Stability of the Financial System. In: Ntalianis, K., Croitoru, A. (eds) Applied Physics, System Science and Computers II. APSAC 2017. Lecture Notes in Electrical Engineering, vol 489. Springer, Cham. https://doi.org/10.1007/978-3-319-75605-9_32
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DOI: https://doi.org/10.1007/978-3-319-75605-9_32
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