An asymmetric model two-dimensional oscillator

We present a novel 2D oscillator with an asymmetric design and investigate its stable vibration utilizing the Ms-DTM method. Initially, we obtain the equations of motion for the proposed system. Subsequently, by employing Taylor expansion of [Formula: see text] and [Formula: see text], the derived nonlinear equations are transformed into linear ones, which we solve analytically using the eigenvalues-eigenfunctions technique. Additionally, we solve the obtained nonlinear system using the Ms-DTM method. Lastly, we examine the stability of the nonlinear system by visualizing the closed nature of the phase portrait.