Numerical Simulation of a Nonlinear, Time-Varying System

This paper investigates the dynamics of a nonlinear, time-varying system described by the differential equation dx/dt= (۶t sin(t) - ۲*t) * x. The system's behavior is analyzed through numerical simulations conducted using MATLAB.The code employs the ode۴۵ function to solve the differential equation for a range of initial conditions, allowing forobservation of the system's sensitivity to initial perturbations. The simulation results demonstrate diverse behaviors,including oscillatory trajectories with varying amplitudes, potential for unbounded growth, and regions of apparentstability. These observations highlight the complex interplay between nonlinearity, time-varying dynamics, andinitial conditions in shaping the system's behavior. Furthermore, the study explores preliminary stability analysisthrough visual inspection of the simulation results. Sustained oscillations and potential unbounded growth in certainscenarios suggest potential instability. This work provides a foundation for further rigorous analysis, includingapplying stability theory and designing robust control strategies to stabilize and regulate the system's behavior in thepresence of inherent nonlinearities and time-varying characteristics.

کلیدواژه ها:

nonlinear ، time-varying ، stability ، MATLAB