Abstract

Financial systems are highly nonlinear and often influenced by investment cycles, market fluctuations, and external financing activities, which can generate complex dynamic behaviors. This paper proposes a new three-dimensional chaotic financial firm model by extending the classical Bouali financial system through the inclusion of a cyclic reinvestment perturbation represented by a sinusoidal nonlinear term. The proposed modification aims to capture state-dependent nonlinear reinvestment feedback in reinvestment decisions caused by changing economic conditions and business cycles. The dynamical characteristics of the model are investigated using equilibrium analysis, local stability theory, Lyapunov exponents, the Kaplan–Yorke dimension, bifurcation analysis, and multistability analysis. Numerical results show that the system possesses three equilibrium points, all of which are unstable under the selected parameter setting. The system exhibits chaotic dynamics confirmed by a positive maximum Lyapunov exponent and a fractal attractor characterized by a Kaplan–Yorke dimension greater than two. Comparative results indicate that the new model demonstrates richer nonlinear dynamical behavior than existing financial firm systems reported in the literature. Furthermore, bifurcation and Lyapunov spectrum analyses disclose multiple transitions between periodic and chaotic states as system parameters vary, while multistability analysis reveals the coexistence of symmetric periodic and chaotic attractors under identical parameter values but different initial conditions. Finally, total amplitude control and offset boosting techniques are implemented to regulate attractor size and position while preserving the underlying chaotic behavior. These findings demonstrate that cyclic reinvestment perturbations significantly enrich the nonlinear dynamics and symmetry properties of financial firm systems, providing a useful framework for studying complex financial behaviors and chaos control.

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