Stationary states of weakly coupled lattice dynamical systems arising in strong competition models

In this work, we consider a weakly coupled lattice dynamical system arising in a strong competition system with bistable nonlinearity. By employing the continuation method developed by MacKay and Sepulchre (1995) [13], we derive estimations of the bounds of the diffusive values d1 and d2 below which the existence of infinite stationary states is proved. These stationary states are continuations from the uncoupled lattice dynamical system.