Finally, stronger mean scaling may underlie another difference from previous work; analyzing networks with (1/N) scaling, other authors have found population-level oscillations via Hopf bifurcations in reduced equations for mean activity [35, 36].
In Sections 3 and 4 we determine the reduced equations of motion for the resonator and register states, respectively.
The outline of the paper is presented in the following way: In Section 2 we present some preliminaries; in Section 3 we present symmetry analysis and reduction; in Section 4 we analyze explicit solution for the reduced equation; in Section 5 we construct Cls for the underlying equation.
However, this traditionary way has quite complicated course of determining coefficients of the two-dimensional reduced equations, and for bifurcation formulae or Liapunov coefficient [6, 8], usually, only the first value is obtained, thus just one single limit cycle in the vicinity of the origin can be found.
The reduced equation is solved to find an analytical formula for the torque in pure elastic case.
"Bifurcation and phase portrait of GKP equation" is devoted to study the topology of both phase portrait and potential curves of the reduced GKP equation for different cases of k u) and also the explicit solutions for each case are obtained.
Since there is no restriction on the distance between the consecutive switching moments of the argument, the reduced difference equation for (5) is of the nonautonomous type given by u k+1)=fbigl k,u k bigr), quad kinmathbb{N}, (10) where (f k,u k))=u k){mathrm{e}}^{(a-bu k))g(k)}).
For obtaining the set of reduced equations, using Eqs.
The corresponding reduced equations are presented in Table 4.
For this purpose, the set of linear differential equations corresponding to the reduced equations described by eqs 47 (section ) was integrated numerically.
