Dynamics and Bifurcation Analysis of a Generalized Three-Dimensional Chaotic Financial System

This paper investigates the dynamics of a three-dimensional nonlinear model of the financial system and the conditions for the emergence of chaotic behavior. The well-known chaotic system with given parameters and initial conditions is considered as a basis. For the initial model, critical points are analyzed, two-dimensional and three-dimensional phase portraits are constructed, and Lyapunov exponents are calculated, which allow confirming the presence of chaos and assessing the degree of sensitivity to initial data. Next, a modification of the system is proposed, consisting of changing the degree of the variable in the second equation. For the group of models obtained, we considered the generalized form of the system, found its critical points, and classified them. At the next stage, a bifurcation analysis was performed: by changing the key parameters of the modified systems, bifurcation diagrams were constructed, and parameter regions corresponding to critical points, periodicity, quasi-periodicity, and chaos were identified. The results demonstrate that the nature of the dynamics depends significantly on both the parameters and the degree of nonlinearity and allow conclusions to be drawn about the mechanisms of chaos in the financial model under consideration.