Harmonic analysis of oscillators through standard numerical continuation tools
For researchers and engineers analyzing or designing nonlinear oscillators in electronic, mechanical, or biochemical systems, this method simplifies harmonic analysis by leveraging existing continuation tools without modification.
The paper presents a numerical continuation method for harmonic analysis of nonlinear periodic oscillators, formulated as a boundary value problem implementable with standard continuation packages like AUTO. The method is demonstrated on an autonomous electronic oscillator (Colpitts) and a non-autonomous mechanical oscillator, aiding analysis and design by tracking curves under harmonic constraints.
In this paper, we describe a numerical continuation method that enables harmonic analysis of nonlinear periodic oscillators. This method is formulated as a boundary value problem that can be readily implemented by resorting to a standard continuation package - without modification - such as AUTO, which we used. Our technique works for any kind of oscillator, including electronic, mechanical and biochemical systems. We provide two case studies. The first study concerns itself with the autonomous electronic oscillator known as the Colpitts oscillator, and the second one with a nonlinear damped oscillator, a non-autonomous mechanical oscillator. As shown in the case studies, the proposed technique can aid both the analysis and the design of the oscillators, by following curves for which a certain constraint, related to harmonic analysis, is fulfilled.