We study a system of $N >>1$ degrees of freedom individually relaxing with a certain rate towards a common equilibrium and coupled via a smooth stationary random Gaussian vector field with both gradient and divergence-free components. We show that generically with increasing the ratio of the coupling strength to the individual relaxation rate the system expériences an abrupt transition from a topologically trivial phase portrait with a single stable equilibrium into topologically non-trivial regime characterized by exponential in N number of equilibria, vast majority of which is expected to be unstable. This picture is suggested to provide a nonlinear analogue of May-Wigner instability transition in mathematical ecology. The analysis invokes statistical properties of the elliptic ensemble of real asymmetric matrices, and raises interesting questions about real eigenvalues of such matrices. \\ \\The presentation will be based on a joint work with Boris Khoruzhenko. arXiv:1509.05737