General Chemotactic Model of Oscillators

We propose a general chemotactic model describing a system of interacting elements. Each element in this model exhibits internal dynamics, and there exists a nonlinear coupling between elements that depends on their internal states. From this model, we derive a simpler model describing the phases and positions of the chemotactic elements by means of center-manifold and phase-reduction methods. We find that, despite its simplicity, the model obtained through this reduction exhibits a rich variety of patterns.