EXACT SOLUTIONS OF CYCLICALLY SYMMETRIC OSCILLATOR EQUATIONS WITH NON-LINEAR COUPLING. PART III: GLOBALLY STABLE SINGLE-FREQUENCY LIMIT CYCLES

✍ Scribed by FOX, DAVID

• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 311 KB
• Volume: 25
• Category: Article
• ISSN: 0098-9886
• DOI: 10.1002/(sici)1097-007x(199705/06)25:3<199::aid-cta963>3.0.co;2-g

✦ Synopsis

Several authors have found very simple exact limit cycle solutions in certain sets of N cyclically symmetric coupled non-linear oscillator equations. In part I of this paper it was shown that the search for sets of equations with similar solutions is made much simpler if the equations are expressed in terms of the normal modes of the unperturbed (linear) system.

In various applications it is desirable that the equations have a limit cycle solution with a single frequency and that this solution be globally stable. It is found here that the transformation of the equations to the unperturbed normal modes can greatly simplify the construction of such systems.