A mathematical model for learning a nonlinear line of attractions is presented in this paper. This model encapsulates attractive fixed points scattered in the state space representing patterns with similar characteristics as an attractive line. The dynamics of this nonlinear line attractor network is designed to operate between stable and unstable states. These criteria can be used to circumvent the plasticity-stability dilemma by using the unstable state as an indicator to create a new line for an unfamiliar pattern. This novel learning strategy utilized stability (convergence) and instability (divergence) criteria of the designed dynamics to induce self-organizing behavior. The self-organizing behavior of the nonlinear line attractor model can helps to create complex dynamics in an unsupervised manner. Experiments performed on CMU face expression database shows that the proposed model can perform pattern association and pattern classification tasks with few iterations and great accuracy.