We investigate a continuous multi-valued dynamical system in R2 of the form x˙∈F(x), where F(x) is a set-valued function and F={f1,f2}. 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, ω-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.