This paper investigates the nonlinear behavior associated with pure intrinsic thermoacoustic (ITA) modes. Unstable ITA modes dominate acoustic modes and drive system instability in certain parameter regimes of a combustor. Frequency of these modes are independently supported by flame dynamics and not influenced by combustor acoustic field. A network model is developed to examine the stability and bifurcation characters of ITA mode. The flame response is modelled using a second-order low pass filter coupled with n - tau model and amplitude response, which mimics the characteristic features of lean fully premixed turbulent bluff-body stabilized flames. Neutral curve expression obtained for anechoic boundary conditions points out that the bifurcation character of ITA mode strongly depends on gain amplitude response. A stability criterion is devised, where positive and negative slopes of gain amplitude response at A= 0 lead to subcritical and supercritical Hopf bifurcations respectively. In the case of subcritical Hopf bifurcation, fold point amplitude is found to depend only on flame response. However, this behavior is not observed for open-open boundary conditions. It is shown that including open-open boundary conditions with non-zero nonlinear time delay brings the effect of combustor parameters on stability boundary and bifurcation character of ITA modes. (C) 2020 The Combustion Institute. Published by Elsevier Inc. All rights reserved.