Cellular differentiation in a developing organism is studied via a discrete bistable reaction-diffusion model. A system of undifferentiated cells is allowed to receive an inductive signal emanating from its environment. Depending on the form of the nonlinear reaction kinetics, this signal can trigger a series of bifurcations in the system. Differentiation starts at the surface where the signal is received and either cells change type up to a given distance or, under other conditions, the differentiation process propagates throughout the whole domain. When the signal diminishes, hysteresis is observed.

We investigate fracture and fragmentation of solids due to impact at low energies using a two-dimensional dynamical model of granular solids. Simulating collisions of two solid disks, we show that, depending on the initial energy, the outcome of a collision process can be classified into two states: a damaged state and a fragmented state, with a sharp transition in between. We give numerical evidence that the transition point between the two states behaves as a critical point, and we discuss the possible mechanism of the transition.