Abstract

A new integer-order chaotic financial system is extended by introducing a simple investment incentive into a three-dimensional chaotic financial system. A four-dimensional fractional-order chaotic financial system is presented by bringing fractional calculus into the new integer-order financial system. By using weighted integral thought, the fractional order derivative's economics meaning is given. The 0-1 test algorithm and the improved Adams-Bashforth-Moulton predictor-corrector scheme are employed to detect numerically the chaos in the proposed fractional order financial system.

Highlights

  • In recent years there has been a high level of interest in the study of chaotic economic systems [1, 2]

  • When the investment incentive intensity d = 0.1, its corresponding phase portraits are strange attractors as shown in Figure 2 and its trajectories in the new (p, s)-plane are Brownian-like as shown in Figure 3(a); that is, the system [3] is chaotic

  • A government is used to employing investment incentive to regulate financial systems

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Summary

Introduction

In recent years there has been a high level of interest in the study of chaotic economic systems [1, 2]. Reference [8] introduced fractional calculus into system [1] and studied its complex dynamics [9]. References [10, 11] studied chaos control of the fractional-order form of system [1]. Reference [12] proposed an uncertain fractal-order form of system [1] and studied its chaos control via adaptive sliding mode. References [15, 16] presented a form of system [1] with time-delayed feedback and studied its dynamics and control. In order to cope with high unemployment or backwardness, in many cases a government would use their policies to stimulate investment which will raise employment, exports, tax revenue, and so on These incentives may take the form of investment grants or investment credit that reduces capital costs for investors.

Caputo Fractional Derivative and Its Economics Meaning
Equilibrium and Stability
Conclusion
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