Reply to the Comment by Johnston

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In the paper by Picard and Johnston," the nature of stochasticity in the Lotka-Volterra systemis investigated. Chaotic orbits in the case of the four modes (7'=2) are extensively studied, show-ing the "nearly ergodic" nature of the four wave system. The case of two modes (T= 1) givesperiodic orbits. The result allows us to expect that the measure of the coherent orbits in the phasespace is infinitesimally small in the case of large nurnber of modes (7'-+cx). (Future work,however, is necessary for the proof.) The subject of our artice" is to study the most probabledrift wave spectra which the weak turbulence theory predicts. 'I"he work in ref. 1 provides onebasis to employ our assumption to lead eq. (15) in ref. 2. Although our article by no means in-tends to cover extensive literatures, the quotation of ref. 1 should have made the arguments inref. 2 more clear and stern. Finally we would like to note the importance of the spontaneous emis-sion term in the long time evolution of the orbits, which the Hamiltonian does not include.
1985-11-15