Ebook Chaos control of a fractional order financial system
Nonlinear chaotic systems have attracted more attention of researchers in various fields of natural sciences. This is because these systems are rich in dynamics, and possess great sensitivity to initial conditions. Since the chaotic phenomenon in economics was first found in 1985, great impact has been imposed on the prominent western economics at present, because the chaotic phenomenon’s occurring in the economic system means that the macro economic operation has in it self the inherent indefiniteness.
Although the government can adopt such macro control measures as the financial policies or the monetary policies to interfere, the effectiveness of the interference is very limited. The instability and complexity make the precise economic prediction greatly limited, and the reasonable prediction behavior has become complicated as well. In the fields of finance, stocks and social economics, because of the interaction between nonlinear factors, with all kinds of economic problems being more and more complicated and with the evolution process from low dimensions to high dimensions, the diversity and complexity have manifested themselves in the internal structure of the system and there exists extremely complicated phenomenon and external characteristics in such a kind of system. So it has become more and more important to study the control of the complicated continuous economic system, and stabilize the instable periodic or stationary solutions, in order to make the precise economic prediction possible ([1]and [2]).
Great interest has been paid to the application of fractional calculus in physics, engineering systems, and even financial analysis ([9] and [10]). The fact that financial variables possess long memories makes fractional modelling appropriate for dynamic behaviors in financial systems. Moreover, the control and synchronization of fractional-order dynamic systems is also performed by various researchers ([11]-[16]). Fractional-order financial system proposed by Wei-Ching Chen in [3] displays many interesting dynamic behaviors, such as fixed points, periodic motions, and chaotic motions.
It has been found that chaos exists in this system with orders less than 3, period doubling and intermittency routes to chaos were found. In this paper, we propose to eliminate the chaotic behaviors from this system, by extending the non-linear feedback control in ODE systems to fractional order systems. This paper is organized as follows: in Section 1, we present the financial system and its fractional version. In Section 2 general approach to feedback control scheme is given, and then we have extended this control scheme to fractional order financial system, numerical results are shown. Finally, in Section 3 concluding comments are given.
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