Switching-mode counterparts of the Rayleigh and Van-der-Pol oscillators

✍ Scribed by Kaplan, B. Z.; Horen, Y.

• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 199 KB
• Volume: 28
• Category: Article
• ISSN: 0098-9886
• DOI: 10.1002/(sici)1097-007x(200001/02)28:1<31::aid-cta92>3.0.co;2-w

✦ Synopsis

The present work deals with two fundamental oscillator models. One of them can be regarded as a switching-mode counterpart of the Rayleigh oscillator, while the other can be regarded as a switchingmode counterpart of the Van-der-Pol oscillator. The models are investigated by several means. Their structure is discussed by treating their circuit models. It is also shown that the related di!erential equations can be solved analytically and explicit forms of exact solutions are attained by employing recursive algebraic processes. The latter solutions are successfully compared to comprehensive direct simulations based on the original di!erential equations. Furthermore, the exhibited solutions of the switching-mode counterparts for small and moderate values of are shown to be closely similar to the solutions of their parent oscillators. Possible applications of the present oscillatory models are discussed. It is argued that the models can favourably serve for simply representing biological and other systems that rely on oscillatory processes.