Dynamic analysis and control of a new hyperchaotic finance system. (English) Zbl 1242.91225

Summary: A new hyperchaotic finance system which is constructed based on a chaotic finance system by adding an additional state variable is presented. The basic dynamical behaviors of this hyperchaotic finance system are investigated, such as the equilibrium, stability, hyperchaotic attractor, Lyapunov exponents, and bifurcation analysis. Furthermore, effective speed feedback controllers and linear feedback controllers are designed for stabilizing hyperchaos to unstable equilibrium points. Numerical simulations are given to illustrate and verify the results.


91G80 Financial applications of other theories
93C95 Application models in control theory
34H10 Chaos control for problems involving ordinary differential equations
Full Text: DOI


[1] 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) · Zbl 1142.91652 · doi:10.1016/j.chaos.2005.08.218
[2] Igor, E., Michael, T.: Dynamic interaction models of economic equilibrium. J. Econ. Dyn. Control 33, 166–182 (2009) · Zbl 1170.91441 · doi:10.1016/j.jedc.2008.04.011
[3] Guégan, D.: Chaos in economics and finance. Annu. Rev. Control 33, 89–93 (2009) · doi:10.1016/j.arcontrol.2009.01.002
[4] Gao, Q., Ma, J.H.: Chaos and Hopf bifurcation of a finance system. Nonlinear Dyn. 58, 209–216 (2009) · Zbl 1183.91193 · doi:10.1007/s11071-009-9472-5
[5] Wijeratne, A.W., Yi, F.Q., Wei, J.J.: Bifurcation analysis in the diffusive Lotka–Volterra system: an application to market economy. Chaos Solitons Fractals 40, 902–911 (2009) · Zbl 1197.35295 · doi:10.1016/j.chaos.2007.08.043
[6] Cai, N., Jing, Y.W., Zhang, S.Y.: Modified projective synchronization of chaotic systems with disturbances via active sliding mode control. Commun. Nonlinear Sci. Numer. Simul. 15(6), 1613–1620 (2010) · Zbl 1221.37211 · doi:10.1016/j.cnsns.2009.06.012
[7] Cai, G.L., Zheng, S., Tian, L.X.: Adaptive control and synchronization of an uncertain new hyperchaotic Lorenz system. Chin. Phys. B 17, 2412–2419 (2008) · doi:10.1088/1674-1056/17/7/014
[8] Vincent, U.E., Guo, R.W.: A simple adaptive control for full and reduced-order synchronization of uncertain time-varying chaotic systems. Commun. Nonlinear Sci. Numer. Simul. 14(11), 3925–3932 (2009) · Zbl 1221.93134 · doi:10.1016/j.cnsns.2008.09.006
[9] Tao, C.H., Liu, X.F.: Feedback and adaptive control and synchronization of a set of chaotic and hyperchaotic systems. Chaos Solitons Fractals 32, 1572–1581 (2007) · Zbl 1129.93043 · doi:10.1016/j.chaos.2005.12.005
[10] Ding, Y.T., Jiang, W.H., Wang, H.B.: Delayed feedback control and bifurcation analysis of Rössler chaotic system. Nonlinear Dyn. 61, 707–715 (2010) · Zbl 1204.93048 · doi:10.1007/s11071-010-9681-y
[11] Zhang, J.X., Tang, W.S.: Control and synchronization for a class of new chaotic systems via linear feedback. Nonlinear Dyn. 58, 675–686 (2009) · Zbl 1183.70075 · doi:10.1007/s11071-009-9509-9
[12] Jian, J.G., Deng, X.L., Wang, J.F.: In: Globally Exponentially Attractive Set and Synchronization of a Class of Chaotic Finance System. Lect. Notes Comput. Sci., vol. 5551, pp. 253–261. Springer, Berlin (2009)
[13] Zhao, X.S., Li, Z.B., Li, S.: Synchronization of a chaotic finance system. Appl. Math. Comput. 217(13), 6031–6039 (2011) · Zbl 1208.91175 · doi:10.1016/j.amc.2010.07.017
[14] Wolf, A., Swift, J.B., Swinney, H.L., John, A.W.: Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985) · Zbl 0585.58037 · doi:10.1016/0167-2789(85)90011-9
[15] Wu, W.J., Chen, Z.Q.: Hopf bifurcation and intermittent transition to hyperchaos in a novel strong four-dimensional hyperchaotic system. Nonlinear Dyn. 60, 615–630 (2010) · Zbl 1194.70036 · doi:10.1007/s11071-009-9619-4
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.