Spatio-Temporal Chaos in a Discrete Turing Model

In this paper, a discrete version of a reaction-diffusion equation, also known as coupled map lattice (CML), which corresponds to the Turing model of morphogenesis is studied. It is shown that CML possesses a hyperbolic property displaying a type of spatio-temporal chaos. Throughout a mathematical background of hyperbolic properties in lattice dynamical systems which are related to spatio-temporal chaos, a mathematical proof is given that the CML obtained from the Turing model possesses such hyperbolic properties. Finally, numerical studies of this finding in varying parameters to present a variety of chaotic behaviors of this system is performed.