du$_{i}$ ( t ) dt = f ( u$_{i}$, v ) = 1 τ ( u α i ( t ) K α u + v $^{α}$( t ) + u α i ( t ) − u$_{i}$ ( t ) + A$_{u}$ ) for i = 1 , . . . , N, (1) dv ( t ) dt = g( u$_{1}$, . . . , u$_{N}$, v ) . (2) Here gene u$_{i}$ activates its own expression by feedback, while the signal v has an inhibitory effect on the expression of the gene u$_{i}$ . Generally, the signal v is released by each cell depending on its gene expression level and the signal abundances at that moment. We adopt Hill-type kinetics for self activation of the gene u$_{i}$ . The parameter α denotes the Hill coefficient, i.e., the cooperativity of its kinetics, while K$_{u}$ is the threshold for the activation of gene u$_{i}$ , and A$_{u}$ is the activation rate of u$_{i}$ by other molecules in the cell. The parameter τ is a time constant of the expression dynamics of u$_{i}$ normalized by that of the signal v . In the present paper, we consider that the timescale of u$_{i}$ is much slower than that of v , so that only fixed point solutions are realized. The assumption on the time scale is biologically reasonable because the gene expression process requires a much longer time than simple catalytic reactions. For numerical simulations, we use the following pa- rameter values; K$_{u}$ = 0 . 1, A$_{u}$ = 0 . 04, α = 2 . 0, τ = 10 . 0. Note that the following results are qualitatively invariant as long as the Hill-coefficient α is larger than unity. Before studying the dynamics of a population of interacting cells, we first survey the single intracellular dynamics Eq. (1) with v given as a constant control parameter. As is shown straightforwardly, the equation has a fixed point solution which exhibits two saddle- node bifurcations with the change in v (Fig. 1). We denote these bifurcation points as v = v ∗ 1 and v = v ∗ $_{2}$, and call the upper branch of the stable state as u$_{(1)}$ (or cell state 1) that is stable at v ≤ v ∗ $_{2}$, and the other lower branch as u$_{(2)}$ (or cell state 2) that is stable at v ≥ v ∗ $_{1}$. In the parameter region v ∗ 1 < v < v ∗ $_{2}$, the bistability of u$_{(1)}$ and u$_{(2)}$ is sustained. As shown in Fig. 1, the only possible stationary states of each cell are u$_{i}$ = u$_{(1)}$ or u$_{i}$ = u$_{(2)}$ . Depending on the value of v and also on the initial condition of u$_{i}$ , each of the 5