Nonlinear oscillations: Amplitude bounds for second-order systems

✍ Scribed by J.K. Aggarwal

• Publisher: Elsevier Science
• Year: 1966
• Tongue: English
• Weight: 517 KB
• Volume: 282
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(66)90377-2

✦ Synopsis

The differential equation describing a driven circuit containing a nonlinear device with the characteristic i = F(e) (where I e I > eo, eF(e) > O) may be reduced, by a transformation, to the pair of differential equations ~ = --f(x) + g(y) + p(t) and ~ = --h(x). Here p(t) is a periodic and bounded driver and f(x), g(y), and h(x) are odd degree polynomials (with leading coefficients positive) which approximate the device characteristic and xh(x) > 0 for all x ~ O. Su~cient conditions are derived for the solution trajectories to be eventually confined in a bounded subset of (x, y) space, thereby giving bounds on periodic and aperiodic oscillations. Other bounding curves which extend to infinity are discussed.