Concentration dynamics and oscillations of K t

A type of the asymptotic solution of a complete set of the kinetic equations does not also depend on the initial concentrations iVa(O) and iVb(O). Therefore, in calculations [21, 25] these values were fixed Na 0) = Nb 0) = 0.1, p = 0.01 and P = 0.1. Note once more that of primary importance of the diffusion-controlled Lotka model are the space dimension d and the relative diffusion parameter k. 

It results in a number of transient regimes to be discussed below. At k = 0 another (quasi-chaotic) kind of solution arises, which has another asymptotic behaviour. 

Solution for a very small parameter n = 0.005 demonstrates a distinctive transient regime with oscillations considerably different at the very beginning from what has been discussed in this Chapter. 

The amplitude of the oscillations K t) is relatively small, the same is true for the amplitudes of the concentration oscillations. The concentration N (t) oscillates around the value of b/K where K is a mean value of K t) whereas Nb t) oscillates around p// respectively. 

The Fourier spectra of concentrations and of the reaction rate are quite similar. The difference is that the strong concentration decay suppresses the Fourier amplitudes at high frequencies. For the concentration motion the change in time of the K (t) acts as an external noise from which the concentration motion selects the main frequencies. 

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