- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 275134, 9 pages
Modeling of Macroeconomics by a Novel Discrete Nonlinear Fractional Dynamical System
Business School, Central South University, Changsha, Hunan 410083, China
Received 2 July 2013; Accepted 12 November 2013
Academic Editor: Zhen Jin
Copyright © 2013 Zhenhua Hu and Wen Chen. 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.
- R. Goodwin, Chaotic Economic Dynamics, Oxford University Press, New York, NY, USA, 1990.
- R. Shone, Economic Dynamics, Cambridge University Press, New York, NY, USA, 2nd edition, 2002.
- J. Stachurski, Economic Dynamics: Theory and Computation, MIT Press, Cambridge, Mass, USA, 2009.
- A. C.-L. Chian, F. A. Borotto, E. L. Rempel, and C. Rogers, “Attractor merging crisis in chaotic business cycles,” Chaos, Solitons & Fractals, vol. 24, no. 3, pp. 869–875, 2005.
- 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.
- I. Podlubny, Fractional Differential Equations, vol. 198 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1999.
- A. A. Kilbas, H. M. Srivastava, and J. J. Trujillo, Theory and Applications of Fractional Differential Equations, vol. 204 of North-Holland Mathematics Studies, Elsevier, Amsterdam, The Netherlands, 2006.
- Y. Xu and Z. He, “The short memory principle for solving Abel differential equation of fractional order,” Computers & Mathematics with Applications, vol. 62, no. 12, pp. 4796–4805, 2011.
- Y. Xu and Z. He, “Synchronization of variable-order fractional financialsystem via active control method,” Central European Journal of Physics, vol. 11, no. 6, pp. 824–835, 2013.
- Y. Xu and Z. He, “Existence and uniqueness results for Cauchy problem of variable-order fractional differential equations,” Journal of Applied Mathematics and Computing, vol. 43, no. 1-2, pp. 295–306, 2013.
- Y. Xu, Z. He, and Q. Xu, “Numerical solutions of fractional advectiondiffusion equations with a kind of new generalized fractional derivative,” International Journal of Computer Mathematics, 2013.
- Y. Xu and O. P. Agrawal, “Models and numerical schemes for generalized van der Pol equations,” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 12, pp. 3575–3589, 2013.
- S. Ma, Y. Xu, and W. Yue, “Numerical solutions of a variable-order fractional financial system,” Journal of Applied Mathematics, vol. 2012, Article ID 417942, 14 pages, 2012.
- A. Kirman and G. Teyssiere, “Microeconomic models for long memory in the volatility of financial time series,” Studies in Nonlinear Dynamics and Econometrics, vol. 5, no. 4, pp. 281–302, 2002.
- K. Yamasaki, L. Muchnik, S. Havlin, A. Bunde, and H. E. Stanley, “Scaling and memory in volatility return intervals in financial markets,” Proceedings of the National Academy of Sciences of the United States of America, vol. 102, no. 26, pp. 9424–9428, 2005.
- V. Anh and A. Inoue, “Financial markets with memory. I. Dynamic models,” Stochastic Analysis and Applications, vol. 23, no. 2, pp. 275–300, 2005.
- F. Garzarelli, M. Cristelli, A. Zaccaria, and L. Pietronero, “Memory effects in stock price dynamics: evidences of technical trading,” http://arxiv.org/abs/1110.5197.
- W.-C. Chen, “Nonlinear dynamics and chaos in a fractional-order financial system,” Chaos, Solitons & Fractals, vol. 36, no. 5, pp. 1305–1314, 2008.
- S. Dadras and H. R. Momeni, “Control of a fractional-order economical system via sliding mode,” Physica A, vol. 389, no. 12, pp. 2434–2442, 2010.
- Z. Wang, X. Huang, and G. Shi, “Analysis of nonlinear dynamics and chaos in a fractional order financial system with time delay,” Computers & Mathematics with Applications, vol. 62, no. 3, pp. 1531–1539, 2011.
- T. Skovranek and I. Podlubny, “Modeling of the national economics in state-space: a fractional calculus approach,” Economic Modelling, vol. 29, no. 4, pp. 1322–1327, 2012.
- G. Jumarie, “Modified Riemann-Liouville derivative and fractional Taylor series of nondifferentiable functions further results,” Computers & Mathematics with Applications, vol. 51, no. 9-10, pp. 1367–1376, 2006.
- D. Gale, The Theory of Linear Economic Models, The University of Chicago Press, Chicago, Ill, USA, 1989.