A Novel Oscillator with Different Nature of the Equilibria and Its Analysis

This paper puts forward a novel three dimensional autonomous oscillator. The dynamics of the proposed system has two squares and one cubic nonlinear term. Rigorous mathematical analysis is done for the proposed oscillator system. The mathematical analysis uncovers the nature of equilibrium points existing within the system. The different nature of the equilibrium points are centre node, saddle node and saddle focus. The analysis is achieved using Routh-Hurwitz criterion and its array formulation. The analysis by Routh Hurwitz method paves the way to identify the oscillatory behaviour of the system. MATLAB simulation environment is used to verify the occurrence of oscillations. MATLAB simulation results corresponds the numerical or mathematical results.