We investigate a continuous multi-valued dynamical system in $\mathbb{R}^{2}$ of the form $\dot{x} \in F(x)$ , where $F(x)$ is a set-valued function and $F=\{f_{1},f_{2}\}$ . Such dynamical systems have applications in various fields, such as mathematical economics. We accurately establish the sufficient conditions for a set of solutions to such a system to exhibit Devaney chaos, $\omega $ -chaos, and infinite topological entropy. Finally, we illustrate these issues with our macroeconomic model, and we highlight the broader applicability of the proposed framework to systems with regime switching.
