The author considers three different two-dimensional networks of nonlocally coupled heterogeneous phase oscillators. Taking the continuum limit of an infinite number of oscillators and using the Ott-Antonsen ansatz he derives the following integrodifferential equation for order parameter-like quantity \(z(\mathbf{r},t)\) \[ \frac{\partial z(\mathbf{r},t)}{\partial t} = - \delta z(\mathbf{r},t) + \frac{1}{2} e^{-i \alpha} \mathcal{G} Z - \frac{1}{2} e^{i \alpha} z^2(\mathbf{r},t) \mathcal{G} \overline{z},\quad (\mathbf{r},t)\in\mathcal{M}\times[0,\infty), \] where \(\mathcal{M}\) is a two-dimensional manifold (e.g. a sphere or a flat torus), \(\delta > 0\) and \(|\alpha|<\pi/2\) are parameters, and \[ (\mathcal{G} z)(\mathbf{r},t) = \int_\mathcal{M} G(\mathbf{r},\mathbf{r'}) z(\mathbf{r'},t) d\mathbf{r'} \] is an integral operator with a specific kernel \(G:\mathcal{M}\times\mathcal{M}\to\mathbb{R}\). For this equation the author carries out numerical investigation of relative fixed points, which represent different coherence-incoherence patterns, also called chimera states. Thus, he obtains stability diagrams for stripe, spot and spiral chimera states and identifies the bifurcations involved in their loss of stability as parameters are varied.