In this work we studied a nonlinear dynamic systems model that helps us explain the complicated behavior of financial markets. This model shows how the prices of financial assets affect each other and investors’ decisions over time, creating feedback loops. Some of these loops can help keep the market stable, while others may make it more unstable.

First, we will check the well-posedness of this model to make sure that all the equations used give meaningful results when tested under realistic conditions. After confirming that our theoretical model works properly, we will study how stable the model is and find the conditions that help the market stay balanced as well as the conditions that can cause bigger swings.

Regulatory policies, intervention rules, or automated market systems will also be part of applying the theoretical study. The main goal of these types of feedback control mechanisms is to improve market stability and prevent extreme price changes; therefore, their use in crises could be helpful for preventing problems in the future.

We will also run many numerical simulations to show how the model behaves under different situations and control strategies. This will give useful insights into financial market behavior and show how mathematical modeling can help the financial industry. Overall, this study helps explain market dynamics and offers a practical way to help institutions understand and predict future market situation.