Qualitative analysis of soft inflation

In this paper we perform a qualitative analysis of the dynamical system resulting from the soft inflation scenario. This allows us to examine the various types of asymptotic behavior displayed by the system; we pay particular attention to the inflationary solutions given by Berkin, Maeda, and Yokoyama [Phys. Rev. Lett. 65, 141 (1990)]. We find that as $\phi \to \infty$, no unique attracting critical point exists, but rather there exists a higher-dimensional set of critical points. It is shown that the solution given by Berkin, Maeda, and Yokoyama is representative of a class of solutions which asymptotically undergoes power-law inflation. Under the assumption that new inflation occurs, we show that, asymptotically, there exists a global attractor. Under the assumption that chaotic inflation occurs, we show that there exists an attractor for finite values of the field $\phi$ and that solutions which inflate will experience infinitely many inflationary eras.