Competitive modes and estimation of ultimate bound sets for a chaotic dynamical financial system

We have investigated the role of competitive mode for the generation of chaotic behavior in a financial dynamical system. Such type of events are very important in the light of stock market crush or volatile behavior. The competitive mode is a good approach other than the fixed point analysis. The character of mode frequencies and the attractor is analyzed numerically . Also, using an analytical method and Lagrange optimization, we were able to calculate the ultimate bound of the chaotic financial system. The method we have presented is simpler and more accurate than other methods that implicitly calculate the final boundary. The estimation of the ultimate bound can be used to study chaos synchronization. Numerical simulations illustrate the analytical results.