Oscillation quenching in coupled different oscillators

When any two different nonlinear oscillators are mutually coupled with each other, their trajectories converge to their own unstable fixed points in a proper coupling strength region. We theoretically analyze the phenomenon of oscillation quenching by mutually coupling the Rössler oscillator with a linear oscillator. Also, we numerically investigate this phenomenon in the mutually coupled system of a Lorenz and a Rössler oscillator. Through these studies, we find that oscillation quenching is a universal behavior that appears when any two different oscillators are mutually coupled.