Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk

@article{Xin2019ModelingDA,
  title={Modeling, discretization, and hyperchaos detection of conformable derivative approach to a financial system with market confidence and ethics risk},
  author={Baogui Xin and Wei Peng and Yekyung Kwon and Yanqin Liu},
  journal={Advances in Difference Equations},
  year={2019},
  volume={2019},
  pages={1-14}
}
We propose a new chaotic financial system by considering ethics involvement in a four-dimensional financial system with market confidence. We present a five-dimensional conformable derivative financial system by introducing conformable fractional calculus to the integer-order system. We propose a discretization scheme to calculate numerical solutions of conformable derivative systems. We illustrate the scheme by testing hyperchaos for the system. 
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References

SHOWING 1-10 OF 100 REFERENCES
0-1 Test for Chaos in a Fractional Order Financial System with Investment Incentive
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
Finite-time stabilizing a fractional-order chaotic financial system with market confidence
TLDR
A robust controller is designed to stabilize the fractional-order chaotic system in a finite time and can be applied to stabilizing other chaotic systems including dynamic economic systems.
Neimark-Sacker Bifurcation in a Discrete-Time Financial System
A discrete-time financial system is proposed by using forward Euler scheme. Based on explicit Neimark-Sacker bifurcation (also called Hopf bifurcation for map) criterion, normal form method and
Dynamic analysis and control of a new hyperchaotic finance system
In this paper, a new hyperchaotic finance system which is constructed based on a chaotic finance system by adding an additional state variable is presented. The basic dynamical behaviors of this
Chaotic Attractors with Fractional Conformable Derivatives in the Liouville–Caputo Sense and Its Dynamical Behaviors
TLDR
A numerical method based on the Adams–Moulton algorithm is employed to approximate the numerical simulations of the fractional-order conformable attractors of type Rabinovich–Fabrikant, Thomas’ cyclically symmetric attractor and Newton–Leipnik.
Uncertain and Stochastic Financial Models with Multiple delays
This paper studies the autonomous uncertain and stochastic systems with multiple delays, which describe a financial system involving the interest rate, the investment demand and the price index. For
Numerical analysis of a fractional-order chaotic system based on conformable fractional-order derivative
Abstract.In this paper, the numerical solutions of conformable fractional-order linear and nonlinear equations are obtained by employing the constructed conformable Adomian decomposition method
Fractional-order Chua’s system: discretization, bifurcation and chaos
In this paper we are interested in the fractional-order form of Chua’s system. A discretization process will be applied to obtain its discrete version. Fixed points and their asymptotic stability are
...
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