Dynamic Analysis and Control of a Financial System with Chaotic Behavior Including Fractional Order

Abstract

This paper presents the results of investigating the dynamics of an economic system with chaotic behavior and a suboptimal control proposal to suppress the chaotic behavior. Numerical results using phase portraits, bifurcation diagrams, Lyapunov exponents, and 0-1 testing confirmed chaotic and hyperchaotic behavior. The results also proved the effectiveness of the control, showing errors below 1%, even in cases where the control design is subject to parametric errors. Additionally, an investigation of the system in fractional order is included, demonstrating that the system has periodic, constant, or chaotic behavior for specific values of the order of the derivative.

Stability Analysis of a Fractional-Order Time-Delayed Solow Growth Model with Environmental Pollution

“…In order to obtain the local stability of system (5), the Equation ( 6) is reduced as Equation (8). If Equation ( 6) is used, the equilibrium point equation is difficult to solve, and the Jacobian determinant at the equilibrium point is also quite complex.…”

“…The study of the complex dynamics of economic systems has become a prominent issue in economics and macroeconomics in recent years. Several nonlinear continuous models have been proposed to explicate the core features of economic data based on the dynamic behavior of the system [6][7][8][9][10][11][12][13][14][15]. The results of investigating the dynamics of an economic system with chaotic behavior and a suboptimal control proposal to suppress the chaotic behavior are presented [8].…”

“…Several nonlinear continuous models have been proposed to explicate the core features of economic data based on the dynamic behavior of the system [6][7][8][9][10][11][12][13][14][15]. The results of investigating the dynamics of an economic system with chaotic behavior and a suboptimal control proposal to suppress the chaotic behavior are presented [8]. A fractional order economic quantity model with time-varying holding cost is discussed in detail with the help of numerical computations [9].…”

Review: Fractal Geometry in Precipitation

“…Nonlinearity and chaos. A dynamical system is nonlinear if the governance law is not simply linear with respect to the temporal variable [52,59]. For example, in the case of the logistic map and geostrophic wind, they have quadratic terms that provide a high complexity in their behavior.…”

“…The scientific community defines these cases as chaotic solutions or simply chaos [61]. A remarkable consequence of the chaotic systems is that phase space presents strange attractors, characterized by fractal measures [59,62]. The Lorenz fractal is a very popular example derived from simplified Navier-Stokes equations [63].…”