Dynamical analysis of a time-delayed financial system with synchronization strategies
Animesh Phukan1, Kaushik Dehingia2,3,4, Hemanta Kumar Sarmah1
1Department of Mathematics, Gauhati University, Guwahati, Assam, India.
Science Progress
|March 30, 2026
Summary
This study models nonlinear financial systems using differential equations. Findings show government debt and investment delays can cause instability, but synchronization control can stabilize the economy.
Area of Science:
- Economic modeling
- Nonlinear dynamics
- Financial mathematics
Background:
- Financial systems exhibit complex, nonlinear behaviors influenced by macroeconomic factors.
- Understanding these dynamics is crucial for economic stability.
Purpose of the Study:
- To investigate nonlinear financial system behavior using an ordinary differential equation model.
- To analyze the impact of government debt and investment time delay on system stability.
- To introduce and validate a synchronization control strategy.
Main Methods:
- Formulation of an ordinary differential equation model with interest rate, investment demand, and price index as state variables.
- Analysis of system equilibria and local stability.
- Investigation of Hopf bifurcation and critical delay effects.
- Implementation of a synchronization control strategy.
Main Results:
- System stability is maintained within a specific government debt range, becoming unstable via Hopf bifurcation at critical points.
- Increased investment time delay beyond a critical magnitude drives system instability.
- The proposed synchronization control strategy effectively counteracts erratic behavior.
Conclusions:
- Government debt and investment time delay are critical parameters influencing financial system stability.
- Synchronization control offers a viable mechanism for stabilizing nonlinear financial systems.
- The model provides insights into managing economic volatility.
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