Nonlinear dynamics and chaos in a fractional-order financial system

Serletic, 1996, Is there chaos in economic series?, Can J Econ, 29, S210, 10.2307/135989

Chen, 1988, Empirical and theoretical evidence of economic chaos, Syst Dyn Rev, 4, 1, 10.1002/sdr.4260040106

Chian, 2000, Nonlinear dynamics and chaos in macroeconomics, Int J Theor Appl Finan, 3, 601, 10.1142/S0219024900000723

Chian, 2005, Attractor merging crisis in chaotic business cycles, Chaos, Solitons & Fractals, 24, 869, 10.1016/j.chaos.2004.09.080

Chian, 2006, Complex economic dynamics: chaotic saddle, crisis and intermittency, Chaos, Solitons & Fractals, 29, 1194, 10.1016/j.chaos.2005.08.218

Schinasi, 1981, Nonlinear dynamic model of short run fluctuations, Rev Econ Stud, 48, 649, 10.2307/2297204

Lorenz, 1993

Sasakura, 1994, On the dynamic behavior of Schinasi’s business cycle model, J Macroecon, 16, 423, 10.1016/0164-0704(94)90015-9

Cesare, 2005, A dynamic IS-LM model with delayed taxation revenues, Chaos, Solitons & Fractals, 25, 233, 10.1016/j.chaos.2004.11.044

Fanti L, Manfredi P. Chaotic business cycles and fiscal policy: an IS-LM model with distributed tax collection lags. Chaos, Solitons & Fractals, 2006, doi:10.1016/j.chaos.2005.11.024.

Huang, 1993

Ma, 2001, Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (I), Appl Math Mech (English Ed), 22, 1240, 10.1023/A:1016313804297

Ma, 2001, Study for the bifurcation topological structure and the global complicated character of a kind of nonlinear finance system (II), Appl Math Mech (English Ed), 22, 1375, 10.1023/A:1022806003937

Arena, 2000

Podlubny, 1999

Ahmad WM, El-Khazali R. Fractional-order dynamical models of love. Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2006.01.098.

Laskin, 2000, Fractional market dynamics, Physica A, 287, 482, 10.1016/S0378-4371(00)00387-3

West, 2002, Fractional Langevin model of memory in financial time series, Phys Rev E, 65, 037106, 10.1103/PhysRevE.65.037106

Panas, 2001, Long memory and chaotic models of prices on the London metal exchange, Resour Policy, 27, 235, 10.1016/S0301-4207(02)00008-9

Hartley, 1995, Chaos in a fractional order Chua’s system, IEEE Trans CAS-I, 42, 485, 10.1109/81.404062

Ahmad, 2003, Chaos in fractional-order autonomous nonlinear systems, Chaos, Solitons & Fractals, 16, 339, 10.1016/S0960-0779(02)00438-1

Grigorenko, 2003, Chaotic dynamics of the fractional Lorenz system, Phys Rev Lett, 91, 034101, 10.1103/PhysRevLett.91.034101

Arena, 2000, Chaotic behavior in noninteger-order cellular neural networks, Phys Rev E, 61, 776, 10.1103/PhysRevE.61.776

Li, 2004, Chaos and hyperchaos in fractional order Rossler equation, Physica A, 341, 55, 10.1016/j.physa.2004.04.113

Gao, 2005, Chaos in the fractional order periodically forced complex Duffing’s equation, Chaos, Solitons & Fractals, 24, 1097, 10.1016/j.chaos.2004.09.090

Sheu LJ, Chen HK, Chen JH, Tam LM. Chaos in a new system with fractional order. Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2005.10.073.

Li, 2004, Chaos in Chen’s system with a fractional order, Chaos, Solitons & Fractals, 22, 443, 10.1016/j.chaos.2004.02.013

Sheu LJ, Chen HK, Chen JH, Tam LM. Chaotic dynamics of the fractionally damped Duffing equation. Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2005.11.066.

Ge ZM, Zhang AR. Chaos in a modified van der Pol system and in its fractional order systems. Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2006.01.098.

Chen JH, Chen WC. Chaotic dynamics of the fractionally damped van der Pol equation. Chaos, Solitons & Fractals, doi:10.1016/j.chaos.2006.05.010.

Caputo, 1967, Linear models of dissipation whose Q is almost frequency independent-II, Geophys J R Astron Soc, 13, 529, 10.1111/j.1365-246X.1967.tb02303.x

Diethelm, 2002, A predictor–corrector approach for the numerical solution of fractional differential equations, Nonlinear Dyn, 29, 3, 10.1023/A:1016592219341

Wolf, 1985, Determining Lyapunov exponents from a time series, Physica D, 16, 285, 10.1016/0167-2789(85)90011-9