Cellular Automata And Its Application To Diffusion Of Innovation

Cellular automata were introduced by von Neumann and Ulam as simple models in which to study biological processes such as self-reproduction. Any system with many identical discrete elements undergoing deterministic local interactions may be modelled as a cellular automaton. Non-trivial cellular automata are obtained when the local evolution is non-linear.The technological innovation acts as an important role in the development of modern economy. And the diffusion of innovation is an important part of the technological innovation. Because the complexity of the diffusion of innovation, the scholars have to just think the special case of the diffusion, in the past. This method is easy for studying, but it can't reflect the truly characteristic of the diffusion of innovation.The first chapter shows the theory of CA, its structure, characteristic and some simple CA. In the second chapter, the paper introduces the development of CA, the CA's actuality and the applications CA in different field. Then, the third chapter explains the meaning of diffusion of technology innovation and introduces some models of diffusion of innovation including the CA models in this field.For reflecting different agents'survival abilities and abilities to influence the market, in the fourth chapter, the paper defines the agent's adaptation. Basing on the influence between the agents, the paper establishes the interaction rule of the agent's state, and presents an opposite one-dimensional cellular automate modeling the diffusion of an innovation in a market. Using this model, the paper discusses the problem of agent's innovations diffusion, and the results show that whether the innovation is adopted by the market is totally independent of the initial number of individuals who adopt the innovation or the size of the market; no matter the innovation is adopted by the market or not, it brings the development for the market.