A new chaotic financial system is proposed by considering ethics involvement in a fourdimensional financial system with market confidence. A five-dimensional conformable derivative financial system is presented by introducing conformable fractional calculus to the integerorder system. A discretization scheme is proposed to calculate numerical solutions of conformable derivative systems. The scheme is illustrated by testing hyperchaos for the system. among interest rates, investments, prices, and savings. Chen [12] presented a fractional form of nonlinear financial system. Wang, Huang and Shen [13] established an uncertain fractional-order form of the financial system. Mircea et al. [14] set up a delayed form of the financial system. Xin, Chen, and Ma [15] proposed a discrete form of financial system. Yu, Cai, and Li [16] extended the
With the awakening of environmental consciousness, more and more firms desire to go “green” by shifting their focus of corporate social responsibility (CSR) from charitable contributions to environmental actions called corporate environmental responsibility (CER). We develop a monopoly differential game to depict optimal corporate strategies of product price, quality, and CER. Using the Hamilton–Jacobi–Bellman (HJB) equation, we analyze optimal feedback equilibrium strategies for pricing and investing in both quality and CER with/without government subsidies. Numerical simulations show that government subsidy can improve CER and profit.
We reconsider the Cournot duopoly problem in light of the theory for long memory. We introduce the Caputo fractional-order difference calculus to classical duopoly theory to propose a fractional-order discrete Cournot duopoly game model, which allows participants to make decisions while making full use of their historical information. Then we discuss Nash equilibria and local stability by using linear approximation.Finally, we detect the chaos of the model by employing a 0-1 test algorithm.
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