Bifurcation Analysis

Bifurcation in optimal retirement ArXiv ID: 2506.02155 “View on arXiv” Authors: Bushra Shehnam Ashraf, Thomas S. Salisbury Abstract We study optimal consumption and retirement using a Cobb-Douglas utility and a simple model in which an interesting bifurcation arises. With high wealth, individuals plan to retire. With low wealth they plan to never retire. At a critical level of initial wealth they may choose to defer this decision, leading to a continuum of wealth trajectories with identical utilities. ...

Synchronization in a market model with time delays ArXiv ID: 2405.00046 “View on arXiv” Authors: Unknown Abstract We examine a system of N=2 coupled non-linear delay-differential equations representing financial market dynamics. In such time delay systems, coupled oscillations have been derived. We linearize the system for small time delays and study its collective dynamics. Using analytical and numerical solutions, we obtain the bifurcation diagrams and analyze the corresponding regions of amplitude death, phase locking, limit cycles and market synchronization in terms of the system frequency-like parameters and time delays. We further numerically explore higher order systems with N>2, and demonstrate that limit cycles can be maintained for coupled N-asset models with appropriate parameterization. ...