Ferroelectric ceramic lead magnesium niobate (PMN) exhibits bistability in its thermal focussing (Chenet al., Appl. Phys. Lett.60, 332 (1992)) which is very sensitive to laser power, specimen temperature, ambient pressure and flow rate of air past the specimen (Scott and Chen,Integrated Ferroelectrics1, 71 (1992)). Under adiabatic switching conditions as many as eight hysteretic multistability loops (transmission versus input power) are observed (Chen and Scott,Integrated Ferroelectrics3, 69 (1993). In the present work at higher input power densities (ca. 10 MW/m2, c.w.) we observe some period multiplication, in qualitative agreement with earlier work on gases (Nakatsukaet al., Phys. Rev. Lett.50, 109 (1983); Harrisonet al., Ibid.51, 562 (1983); Firth and Al-Saidi,Ibid.53, 258 (1984). However, our data do not manifest the required symptoms of Feigenbaum bifurcations (a stochastic rather than chaotic power spectrum evolves, and the successive lengths of control parameter between bifurcations are not Feigenbaum-like). The switching characteristics can be quantitatively described by a system of May-Leonard oscillators, whose principal characteristics is the exact geometric progression of successive switching events.