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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 876298, 10 pages
0-1 Test for Chaos in a Fractional Order Financial System with Investment Incentive
1Nonlinear Science Center, School of Economics and Management, Shandong University of Science and Technology, Qingdao 266590, China
2Nonlinear Dynamics and Chaos Group, School of Management, Tianjin University, Tianjin 300072, China
Received 5 September 2013; Accepted 25 September 2013
Academic Editor: Luca Guerrini
Copyright © 2013 Baogui Xin and Yuting Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- A. C.-L. Chian, E. L. Rempel, and C. Rogers, “Complex economic dynamics: chaotic saddle, crisis and intermittency,” Chaos, Solitons and Fractals, vol. 29, no. 5, pp. 1194–1218, 2006.
- B. Xin, J. Ma, and Q. Gao, “The complexity of an investment competition dynamical model with imperfect information in a security market,” Chaos, Solitons and Fractals, vol. 42, no. 4, pp. 2425–2438, 2009.
- D. Huang and H. Li, Theory and Method of the Nonlinear Economics, Sichuan University, Chengdu, China, 1993, (Chinese).
- J.-H. Ma and Y.-S. Chen, “Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (I),” Applied Mathematics and Mechanics, vol. 22, no. 11, pp. 1240–1251, 2001.
- J.-H. Ma and Y.-S. Chen, “Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (II),” Applied Mathematics and Mechanics, vol. 22, no. 12, pp. 1375–1382, 2001.
- J. Ma and T. Bangura, “Complexity analysis research of financial and economic system under the condition of three parameters change circumstances,” Nonlinear Dynamics, vol. 70, pp. 2313–2326, 2012.
- Q. Gao and J. Ma, “Chaos and Hopf bifurcation of a finance system,” Nonlinear Dynamics, vol. 58, no. 1-2, pp. 209–216, 2009.
- W.-C. Chen, “Nonlinear dynamics and chaos in a fractional-order financial system,” Chaos, Solitons and Fractals, vol. 36, no. 5, pp. 1305–1314, 2008.
- B.-G. Xin, T. Chen, and Y.-Q. Liu, “Complexity evolvement of a chaotic fractional-order financial system,” Acta Physica Sinica, vol. 60, no. 4, Article ID 048901, 2011.
- M. S. Abd-Elouahab, N.-E. Hamri, and J. Wang, “Chaos control of a fractional-order financial system,” Mathematical Problems in Engineering, vol. 2010, Article ID 270646, 18 pages, 2010.
- I. Pan, A. Korre, S. Das, and S. Durucan, “Chaos suppression in a fractional order financial system using intelligent regrouping PSO based fractional fuzzy control policy in the presence of fractional Gaussian noise,” Nonlinear Dynamics, vol. 70, pp. 2445–2461, 2012.
- Z. Wang, X. Huang, and H. Shen, “Control of an uncertain fractional order economic system via adaptive sliding mode,” Neurocomputing, vol. 83, pp. 83–88, 2012.
- G. Mircea, M. Neamtu, O. Bundau, and D. Opris, “Uncertain and stochastic financial models with multiple delays,” International Journal of Bifurcation and Chaos, vol. 22, no. 6, Article ID 1250131, 19 pages, 2012.
- B. Xin, T. Chen, and J. Ma, “Neimark-sacker bifurcation in a discrete-time financial system,” Discrete Dynamics in Nature and Society, vol. 2010, Article ID 405639, 12 pages, 2010.
- W.-C. Chen, “Dynamics and control of a financial system with time-delayed feedbacks,” Chaos, Solitons and Fractals, vol. 37, no. 4, pp. 1198–1207, 2008.
- W.-S. Son and Y.-J. Park, “Delayed feedback on the dynamical model of a financial system,” Chaos, Solitons and Fractals, vol. 44, no. 4-5, pp. 208–217, 2011.
- Y. Ding, W. Jiang, and H. Wang, “Hopf-pitchfork bifurcation and periodic phenomena in nonlinear financial system with delay,” Chaos, Solitons & Fractals, vol. 45, pp. 1048–1057, 2012.
- H. Yu, G. Cai, and Y. Li, “Dynamic analysis and control of a new hyperchaotic finance system,” Chaos, Solitons & Fractals, vol. 45, pp. 1048–1057, 2012.
- M. Dinica, “The real options attached to an investment project,” Economia, Seria Management, vol. 14, pp. 511–518, 2011.
- B. Xin, T. Chen, and Y. Liu, “Synchronization of chaotic fractional-order WINDMI systems via linear state error feedback control,” Mathematical Problems in Engineering, vol. 2010, Article ID 859685, 10 pages, 2010.
- B. Xin, T. Chen, and Y. Liu, “Projective synchronization of chaotic fractional-order energy resources demand-supply systems via linear control,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, pp. 4479–4486, 2011.
- X. C. Li and W. Chen, “Nested meshes for numerical approximation of space fractional differential equations,” The European Physical Journal, vol. 193, no. 1, pp. 221–228, 2011.
- X. Li and W. Chen, “Analytical study on the fractional anomalous diffusion in a half-plane,” Journal of Physics A, vol. 43, no. 49, Article ID 495206, 2010.
- S. Chen and X. Jiang, “Analytical solutions to time-fractional partial differential equations in a two-dimensional multilayer annulus,” Physica A, vol. 391, no. 15, pp. 3865–3874, 2012.
- X. Jiang and H. Qi, “Thermal wave model of bioheat transfer with modified Riemann-Liouville fractional derivative,” Journal of Physics A, vol. 45, Article ID 485101, 2012.
- W. Deng, “Numerical algorithm for the time fractional Fokker-Planck equation,” Journal of Computational Physics, vol. 227, no. 2, pp. 1510–1522, 2007.
- W. Deng, “Smoothness and stability of the solutions for nonlinear fractional differential equations,” Nonlinear Analysis: Theory, Methods and Applications, vol. 72, no. 3-4, pp. 1768–1777, 2010.
- K. Diethelm, N. J. Ford, and A. D. Freed, “Detailed error analysis for a fractional Adams method,” Numerical Algorithms, vol. 36, no. 1, pp. 31–52, 2004.
- K. Diethelm, N. J. Ford, and A. D. Freed, “A predictor-corrector approach for the numerical solution of fractional differential equations,” Nonlinear Dynamics, vol. 29, no. 1–4, pp. 3–22, 2002.
- G. A. Gottwald and I. Melbourne, “A new test for chaos in deterministic systems,” Proceedings of the Royal Society A, vol. 460, no. 2042, pp. 603–611, 2004.
- G. A. Gottwald and I. Melbourne, “On the implementation of the 0-1 test for chaos,” SIAM Journal on Applied Dynamical Systems, vol. 8, no. 1, pp. 129–145, 2009.
- G. A. Gottwald and I. Melbourne, “On the validity of the 0-1 test for chaos,” Nonlinearity, vol. 22, no. 6, pp. 1367–1382, 2009.
- I. Falconer, G. A. Gottwald, I. Melbourne, and K. Wormnes, “Application of the 0-1 test for chaos to experimental data,” SIAM Journal on Applied Dynamical Systems, vol. 6, no. 2, pp. 395–402, 2007.
- S. Devi, S. Singh, and A. Sharma, “Deterministic dynamics of the magnetosphere: results of the 0-1 test,” Nonlinear Processes in Geophysics, vol. 20, pp. 11–18, 2013.
- G. Litak, A. Syta, and M. Wiercigroch, “Identification of chaos in a cutting process by the 0-1 test,” Chaos, Solitons and Fractals, vol. 40, no. 5, pp. 2095–2101, 2009.
- G. Litak, A. Syta, M. Budhraja, and L. M. Saha, “Detection of the chaotic behaviour of a bouncing ball by the 0-1 test,” Chaos, Solitons and Fractals, vol. 42, no. 3, pp. 1511–1517, 2009.
- D. Bernardini, G. Rega, G. Litak, and A. Syta, “Identification of regular and chaotic isothermal trajectories of a shape memory oscillator using the 0-1 test,” Journal of Multi-Body Dynamics K, vol. 227, no. 1, pp. 17–22, 2013.
- K. Sun, X. Liu, and C. Zhu, “The 0-1 test algorithm for chaos and its applications,” Chinese Physics B, vol. 11, Article ID 110510, 2010.
- L.-G. Yuan and Q.-G. Yang, “A proof for the existence of chaos in diffusively coupled map lattices with open boundary conditions,” Discrete Dynamics in Nature and Society, vol. 2011, Article ID 174376, 16 pages, 2011.
- K. Webel, “Chaos in German stock returns—new evidence from the 0-1 test,” Economics Letters, vol. 115, no. 3, pp. 487–489, 2012.
- L. Zachilas and I. N. Psarianos, “Examining the chaotic behavior in dynamical systems by means of the 0-1 test,” Journal of Applied Mathematics, vol. 2012, Article ID 681296, 14 pages, 2012.
- B. Xin and Y. Li, “Bifurcation and chaos in a price game of irrigation water in a coastal irrigation district,” Discrete Dynamics in Nature and Society, vol. 2013, Article ID 408904, 10 pages, 2013.
- S. Vahedi and M. S. M. Noorani, “Analysis of a new quadratic 3D chaotic attractor,” Abstract and Applied Analysis, vol. 2013, Article ID 540769, 7 pages, 2013.
- B. Krese and E. Govekar, “Nonlinear analysis of laser droplet generation by means of 0-1 test for chaos,” Nonlinear Dynamics, vol. 67, no. 3, pp. 2101–2109, 2012.
- Y. Kim, “Identification of dynamical states in stimulated Izhikevich neuron models by using a 0-1 test,” Journal of the Korean Physical Society, vol. 57, no. 6, pp. 1363–1368, 2010.
- A. M. Fraser and H. L. Swinney, “Independent coordinates for strange attractors from mutual information,” Physical Review A, vol. 33, no. 2, pp. 1134–1140, 1986.
- Y. Yu, H.-X. Li, S. Wang, and J. Yu, “Dynamic analysis of a fractional-order Lorenz chaotic system,” Chaos, Solitons and Fractals, vol. 42, no. 2, pp. 1181–1189, 2009.