Abstract
The complex dynamical behavior of a finance system is investigated in this paper. The Ruelle–Takens route to chaos and strange nonchaotic attractors (SNA) are found through numerical simulations. Then the system with time-delayed feedback is considered and the stability and Hopf bifurcation of the controlled system are investigated. This research has important theoretical and practical meanings.
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Chian, A.C.-L., Rempel, E.L., Rogers, C.: Complex economic dynamics: Chaotic saddle, crisis and intermittency. Chaos Solitons Fractals 29(5), 1194–1218 (2006)
Fanti, L., Manfredi, P.: Chaotic business cycles and fiscal policy: An IS-LM model with distributed tax collection lags. Chaos Solitons Fractals 32(2), 736–744 (2007)
Grebogi, C., Ott, E., Pelikan, S., Yorke, J.A.: Strange attractors that are not chaotic. Physica D Nonlinear Phenom. 13(1–2), 261–268 (1984)
Heagy, J.F., Hammel, S.M.: The birth of strange nonchaotic attractors. Physica D Nonlinear Phenom. 70(1–2), 140–153 (1994)
Prasad, A., Biswal, B., Ramaswamy, R.: Strange nonchaotic attractors in driven excitable systems. Phys. Rev. E 68, 037201 (2003)
Yalcınkaya, T., Lai, Y.-C.: Blowout bifurcation route to strange nonchaotic attractors. Phys. Rev. Lett. 77(25), 5039–5042 (1996)
Khovanov, I.A., Khovanova, N.A., McClintock, P.V.E., Anishchenko, V.S.: The effect of noise on strange nonchaotic attractors. Phys. Lett. A 268(46), 315–322 (2000)
Wenping, H., Guolin, F., Xinquan, G., Jifan, C.: Dynamics of the Lorenz system under quasiperiodic driving. Acta Phys. Sin. 55(06), 3175–3179 (2006) (in Chinese)
Junhai, M., Yushu, C.: Study for the bifurcation topological structure and the global complicated character of a kind of non-linear finance system (I). Appl. Math. Mech. 11(22), 1119–1128 (2001) (in Chinese)
Junhai, M., Yushu, C.: Study for the bifurcation topological structure and the global complicated character of a kind of non-linear finance system (II). Appl. Math. Mech. 12(22), 1236–1242 (2001) (in Chinese)
Junhai, M.: The Reconstruction Technology of Complex Nonlinear System. Tianjin University Press, Tianjin (2005)
Chen, W.-C.: Dynamics and control of a financial system with time-delayed feedbacks. Chaos Solitons Fractals 37(4), 1198–1207 (2008)
Chen, W.-C.: Nonlinear dynamics and chaos in a fractional-order financial system. Chaos Solitons Fractals 36(5), 1305–1314 (2008)
Yan, X.-P., Zhang, C.-H.: Hopf bifurcation in a delayed Lokta—Volterra predator—prey system. Nonlinear Anal. Real World Appl. 9(1), 114–127 (2008)
Ruan, S., Wei, J.: On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. 10, 863–874 (2003)
Yushu, C.: Bifurcation and Chaos Theory of Nonlinear Vibration Systems. Higher Education Press, Beijing (1995)
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Gao, Q., Ma, J. Chaos and Hopf bifurcation of a finance system. Nonlinear Dyn 58, 209–216 (2009). https://doi.org/10.1007/s11071-009-9472-5
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DOI: https://doi.org/10.1007/s11071-009-9472-5