Limit cycles in highly non-linear differential equations

This paper is concerned with both small-amplitude and large-amplitude limit cycle bifurcations of planar differential systems. The analysis is not res tricted to minimal models with few non-linear terms, in fact, the novel app roach adopted here is to consider differential equations containing highly non-linear terms in both the damping and restoring coefficients. The maximu m number of limit cycles which may be bifurcated in a small region of the o rigin is given for certain classes of the more generalised mixed (Rayleigh- Lienard) oscillator equations of the form (x) double over dot + (f(x) + h(( x)) over dot)(x) over dot + g(x) = 0. Certain mechanical systems are invest igated. (C) 1999 Academic Press.